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THE 



ELEMENTS OE LOGIC: 



ADAPTED TO THE 



CAPACITY OF YOUNGER STUDENTS, 



DESIGNED FOR ACADEMIES AND THE HIGHER 
'CLASSES OF COMMON SCHOOLS. 



By CHARLES OTRUE, D.D. 



Nihil difficile amanti.— Cicero. -, _ 



. 






THIRD EDITION, REVISED. 

Ntw gork: ...*' 

PUBLISHED BY CARLTON & PORTER, 

200 MULBERRY-STREET. 

I VIS ON, PHINNEY & CO., 

48 AND 50 "WALKER-STREET. 



^ C '.fs 



Entered according to Act of Congress, in the year 1860. 

By CARLTON & PORTER, 

in the Clerk's Office of the District Court of the United States for 
the Southern District of New-York. 



2-/ X- f & 



\ 



PREFACE. 



Logic, as a science, is simple and 
limited. Most modern treatises upon the 
subject have erred, by extending it be- 
yond its proper department, on the one 
hand, and by excluding it from its legiti- 
mate province on the other. By some it 
has been made to occupy the ground of 
mental science or of rhetoric ; by others it 
has been denominated, " cm art of reason- 
ing," as if there were any sound reasoning 
which is not logical, while others have 
claimed for it the unlimited sphere of 
teaching "the right use of reason." These 
errors have been exposed by Archbishop 



Whately, and the true nature and ap- 
propriate office of logic have been ex- 
plained and vindicated. His learned and 
able treatise has obtained favor in the 
universities of Great Britain and the 
United States, and will go far, undoubt- 
edly, to revive and extend a neglected, 
but invaluable science. The principles of 
that work, which are none other than 
those of Aristotle, have beeji adopted as 
the basis of the present volume. 

The treatise now presented to the 
public is designed for a department 
hitherto unoccupied. 

A science, so rudimentary in its prin- 
ciples, and so extensive in its applications, 
ought to be studied with the common 
elements of learning. Nor, when prop- 
erly explained, will it be found any more 
difficult to the younger student than 
grammar or arithmetic. It will not task 



PEEFACE. 5 

the powers beyond what is desirable in 
salutary discipline, while its tendency to 
promote a habit of thinking will be 
greater than that of any other science. 
Indeed, logic must be studied early, and 
rendered perfectly familiar, in' order to be 
of much practical utility in the business 
of life. It is so long postponed in existing 
systems of education, and, after all, so 
superficially studied, that there is scarcely 
one educated man in a thousand w r ho pro- 
fesses to be master of logic. 

This work, though simple in its arrange- 
ment, embraces all that is essential to 
logic, while everything which does not 
strictly and necessarily come within the 
appropriate province of the science has 
been excluded. Collateral matter and 
discursive explanations have been avoided, 
as rather calculated to embarrass and con- 
fuse the youthful mind. The principles 



6 PKEFACE. 

and rules of the science have been stated 
distinctly, and illustrated by a variety of 
examples. If any further explanation is 
necessary the enlightened teacher can 
easily supply it. The great points will 
thus stand out prominently to view, and 
all that is added by way of comment will 
be associated with them in the mind. 
The attention of the learner will not be 
distracted by many particulars, nor the 
memory encumbered with unessential 
matter. 

Boston, August 14, 1840. 



PREFACE TO THE REVISED EDITION. 



The first edition of this book has been 
used chiefly in academies of a high grade 
and as a manual in some colleges. The 
improvements in this edition will make it 
still more acceptable to advanced students, 
while it will be no less adapted to the 
object for which it was originally de- 
signed, namely, to follow immediately 
after grammar in all schools where the 
higher branches are commenced. Will 
teachers of grammar schools now give 
this book a trial, and make known to 
the public the results of the experiment? 
Consider: Will it not be of the greatest 



8 PREFACE TO THE REVISED EDITION. 

advantage to form the habit in early 
life of analyzing one's process of thought 
in reasoning, and especially observing 
whether the reason given for an opinion 
is a general reason. For example: It is 
of itself no proof, that you are not at 
the scene of a murder, because you are 
here. Indeed ! what other proof is neces- 
sary? Clearly this general principle — 
that no being but God can be in two 
places at the same time. Without this 
as a major premise, your alibi as a minor 
premise answers no purpose. To be sure 
this principle is implied in the minor 
premise, and it happens to be a sound 
one ; but how often in practical life do 
we imply in our statements a general 
principle which is not sound ; but its 
unsoundness escapes us, because we are 
not in the habit of considering it dis- 
tinctively. It would be easy enough 



PEEFACE TO THE REVISED EDITION. 9 

to give illustration of this from any 
political or religious newspaper that 
comes to hand. I insist, therefore, that 
a science so pertinent to every-day 
practical life should not be excluded 
from elementary studies, but should be 
taught in every grammar school. 

The most important improvements in 
this edition are the Analytical Outline, 
the Chapter on Distinctions of Reason- 
ing, and the Essay on the Philosophy of 
Induction. 

New Yoke, October, 1860. 



CONTENTS. 



Fags 

Analytical Outline 13 

PART I.— ON TERMS. 

Section 

I. Different Kinds of Terms 23 

II. Opposition of Terms 26 

III. Species and Genus 28 

IY. Division 30 

Y. Definition 31 

PART II.— PROPOSITIONS. 

I. Parts of a Proposition 35 

II. Distinction of Propositions 31 

III. Further Distinctions 41 

IY. Distribution of Terms of Propositions 43 

Y. Opposition. 46 

YI. Conversion 52 

PART III— ARGUMENTS. 

Definition of Arguments 5t 

I. Syllogisms 58 

II. Rules of Syllogism 61 

HI. Irregular Syllogisms Tl 

IY. Hypothetical Syllogism. — Dilemma 11 

Y. Distinctions of Reasoning. , 83 



12 CONTENTS. 



PART IV.— FALLACIES. 

Page 

Distinction of Fallacies 95 

I. Logical Fallacies 98 

II. Material Fallacies 102 

SUPPLEMENT. 

I. Moods and Figures op Syllogisms 10*7 

II. Reduction 114 

Questions in Review 120 

APPENDIX. 

I. Dissertation on Induction. 121 

II. Miscellaneous Examples for Practice : 152 

Supposed Exceptions to Rules 168 



ELEMENTS OF LOGIC. 



INTRODUCTION. 

ANALYTICAL OUTLINE. 

1. Logic is the science of inference; it teaches 
how one judgment may be inferred from other 
judgments. To reason is to infer, hence it is 
usually called the science of reasoning. 

2. It assumes that every mind conceives in- 
tuitively some ideas or judgments which are 
at once primary and certain ; otherwise we could 
have no foundation for inference ; and to infer 
one idea or judgment from others would give 
no certainty. 

These ideas are called first truths. They are 
given by the senses, the consciousness, and the 
reason, and are innumerable. I exist. There 
is an external vjorld. This body is solid, ex- 



14 ELEMENTS OF LOGIC. 

tended, round, red, warm, or cold, are first 
truths. 

3. At first these ideas are particular, but 
afterward the mind unites those which are the 
same in some respect into classes by simple ad- 
dition. This is called generalization. To ex- 
press this we no longer say, This tody, and 
that tody, and yonder body, etc., but body. 
Med body would be a lower class made up of 
this red thing, that red thing, etc. 

4. It is evident, furthermore, that in order to 
reason the mind must have some general ideas, 
or judgments, that are conceived intuitively, 
and not formed by mere addition or generali- 
zation ; for if you make a class by adding all 
the individuals, you gain nothing by drawing 
one or more out again. These general ideas are 
called first principles, or axioms, and are the 
offspring of the reason. Some of the earliest 
are these : Every body is in space. JYo event 
happens without a cause. Like material causes 
produce like effects. 

5. It is the province of psychology to explain 
under what circumstances these primary ideas 
are given by the senses, the consciousness, and 
the reason; but logic assumes their existence 



ANALYTICAL OUTLINE. 15 

as the indispensable basis of inference, and its 
appropriate office is to explain in what way 
we infer one judgment from another. 

6. The process of reasoning when completed 
is found to be simply this : Something is predi- 
cated, that is, affirmed or denied of a class ; an 
individual is affirmed to belong to this class, 
and then, of course, the same thing can be af- 
firmed or denied of that individual. 

In whatever form a sound argument is ex- 
pressed, it may always be shown to involve this 
process, and every unsound argument deviates 
from it. In reasoning we always proceed from 
generals to particulars, and never from particu- 
lars to generals, for this is impossible, as it would 
be to draw out what was never put in. A gene- 
ral principle, to be sure, may be inferred from one 
still more general ; but in relation to that more 
general principle it is only a particular ; it is a 
class in a class of classes — a species under a 
genus. For example, the general law of ter- 
restrial gravity is an inference, not from par- 
ticular instances of bodies falling to the earth, 
but from a more general law, which these par- 
ticulars indicate. This is an instance of in- 
duction. 



16 ELEMENTS OF LOGIC. 

7. As induction has been supposed to be a 
mode of reasoning opposite to deduction, let 
us take a simple and common case. I infer that 
heat to such a degree as will cause the mercury 
in the thermometer to rise to the point marked 
two hundred and twelve degrees on Fahrenheit's 
thermometer will always cause water to boil; 
in other words, it is proved by induction to 
be a law of nature that two hundred and 
twelve degrees Fahrenheit will cause water to 
boil. 

Now this conclusion is not drawn from any 
number of instances of the boiling of water, but 
from a few instances combined with the prin- 
ciple that like cause will produce like effects ; 
for if this principle were not true, then forty 
thousand instances of water boiling by such a 
degree of heat would not prove that another 
case would happen, no more than finding forty 
thousand clovers bearing three leaves only 
would prove that clover always has only three 
leaves; or finding forty different varieties of 
cloven-footed animals marked with horns would 
prove that swine must have horns. But now I 
know that like causes will produce like effects, 
and I know also by observation that two hund- 



ANALYTICAL OUTLINE. 17 

red and twelve degrees Fahrenheit did once, 
or twice, or thrice cause water to boil, and I 
therefore infer that it will always cause water 
to boil. Admit the premises and the conclusion 
is unavoidable ; and to do this is simply to 
affirm something of a class, then to refer an in- 
dividual to that class, and then to affirm the 
same thing of that individual. 

Now the first premise is a general principle, 
which is intuitively true. The only question is 
about the second premise, namely, whether two 
hundred and twelve degrees Fahrenheit was the 
cause of boiling in the instances observed. 

You may now prove this by another argu- 
ment made up of another intuitive principle, 
and an observed fact, or perhaps by two argu- 
ments, thus : no event happens without a cause ; 
the boiling of water is an event, therefore it 
happened not without cause ; in other words, it 
happened by some cause. What cause? 

It is a presumption of reason that those 
things which immediately and invariably pre- 
cede a certain event are its cause, or include its 
cause. 

Now observation and experiment have shown 
when two hundred and twelve degrees Fahren- 



18 ELEMENTS OF LOGIC. 

heit was present water invariably and imme- 
diately boiled; and when it was absent, the 
other circumstance remaining just as before, it 
did not boil. Hence it is concluded that it was 
the cause of the boiling in these cases. 

Thus the second premise of the main argu- 
ment being proved, the first conclusion is estab- 
lished, namely, that two hundred and twelve 
degrees Fahrenheit is always the cause of water 
boiling. 

Every case of induction proper proceeds 
upon the same grounds and in the same way. 
It is, therefore, evident induction is no excep- 
tion to the rule that inference is always from 
generals to particulars, and not from particulars 
to generals. 

8. Seasoning by analogy proceeds in the 
same way ; the difference is only in the char- 
acter of the first premise, which is, that similar 
causes are likely to produce similar effects, or 
that things which agree in certain attributes or 
relations are likely to agree in certain other at- 
tributes or relations. Thus we reason by analo- 
gy that Jupiter is likely to be inhabited as well 
as the earth, and that retribution may be ex- 
pected in a future life as well as in this. 



ANALYTICAL OUTLINE. 19 

9. Reasoning a priori and a posteriori are 
not different modes of reasoning, but arguments 
differing in the character of one of the premises : 
in the one we reason from antecedents, and 
in the other from consequents. From the idea 
of perfection, as an antecedent in the human 
mind, Des Cartes argued a priori for the exist- 
ence of a Perfect Being ; and Paley, from the 
marks of contrivance in the world as an effect, 
proved a posteriori an intelligent Creator. 

10. It will be seen that the value of any con- 
clusion depends upon the degree of certainty 
which belongs to the premises. If they are cer- 
tain the conclusion is certain ; if they are prob- 
able the conclusion is only probable. This is 
the only distinction between mathematical and 
moral or practical reasoning ; nor does this al- 
ways exist, for some moral arguments may claim 
premises that are absolutely certain. 

11. It remains only to observe that the syl- 
logism is merely a certain convenient mode of 
stating an argument ; and that is the most per- 
fect syllogism which is framed so as to make 
the true process of inference the most apparent. 
The above instance of induction would be stated 
as a syllogism, thus : 



20 ELEMENTS OF LOGIC. 

Like causes will ever produce like effects. 
Two hundred and twelve degrees Fahrenheit is like 
the cause that produced boiling of water; 
Therefore, it will ever produce the like effect. 

Or thus : 

Whatever caused the boiling of water once will always 
cause it. 

Heat 212° Fahrenheit caused the boiling of water 
once; 

Therefore, it will always cause it. 

12. Analyzing a syllogism, for example : 

All men are mortal. 
Mohammed was a man ; 
Therefore, Mohammed was mortal : 

we find that it is made up of three propositions ; 
that each proposition contains two terms and a 
copula, expressing an agreement or disagreement 
of the terms. Each term denotes an idea, as all 
men, mortal, Mohammed; each proposition ex- 
presses a judgment as to the relation of two terms 
to each other, and the last of these propositions 
is an inference from the other two judgments. 
The three operations of mind concerned in rea- 



ANALYTICAL OUTLINE. 21 

soiling are therefore simple apprehension, judg- 
ment, and inference. 

13. Language serves to express these mental 
operations, but the mind has ideas, judgments, 
and inferences before it has language, inasmuch 
as a sign must of necessity be subsequent to the 
thing signified. 

14. From this analysis it appears that logic 
enters into the vital processes of the mind, and 
conducts it from the known to the unknown. 
A demonstration is essentially a discovery : the 
propositions in a book of geometry are involved 
in the axioms and definitions on the first page, 
but to draw them out is as much a discovery to 
the mathematician as the continent of America 
was to Columbus. 



SYNTHESIS OF LOGIC* 



PART I. 



OIST TEEMS. 

1. The first part of Logic treats of Terms. 

A Term is one or more words expressing a 
thing, or what is thought of a thing ; as, 

Grass is green. Grass is a terra, and green is 
a term. 

The sun shines brightly. The sun is a term, 
and shines brightly is a term. 

SECTION I. 

DIFFERENT KINDS OF TERMS. 

2. A Singular Term expresses only one indi- 
vidual; as, 

Boston, Connecticut River, this rock, the discoverer of 
America. 

* Younger students commence here. 



24 ELEMENTS OF LOGIC. 

3. A Common Term is one which is not con- 
fined to a single object, as City, which may 
apply to Boston and to all other cities. 

Eock, Kiver, Conqueror, Mariner. 
Strong, Happy, "Wise, Great, Balmy, Dark. 

4. A Relative Term expresses an object 
that is related to another object ; as. Husband, 
which is related to wife. Parent, which im- 
plies offspring. 

Eider, Euler, Brother, Servant, Magistrate. 

5. An Absolute Term expresses a thing con- 
sidered by itself, without reference to any other 
thing; as, 

Eiver, Mountain, Power, Wisdom. 

6. A Positive Term expresses a thing as 
actually existing; as, 

Sight, Seeing, Speech, A man speaking. 

7. A Privative Term is one which expresses 
the absence of an attribute from a thing capable 
of it; as, a blind man, which denotes the ab- 
sence of the power to see. 

A lame stag, A leafless oak, A dead plant. 



DIFFERENT KINDS OF TERMS. 25 

8. A Negative Teem denotes the absence 
of an attribute from a subject, which is not 
capable of it at all ; as, 

A dumb statue, Lifeless marble, Silent dews. 

9. An Abstract Term is one which ex- 
presses a quality, without reference to any 
subject in which it may be found ; as, 

Roundness, Hardness, Wisdom, Justice, Folly. 

10. A Concrete Term expresses both the 
attribute and the object to which it belongs ; 
as, wrong, which expresses both an action and 
its quality ; ruler, which indicates an agent and 
his office. 

Philosopher, Governor, Wise, Energetic, Hard. 

11. An Indefinite Term is one which does 
not define or mark out an object, and has the 
particle- not attached to it, expressed or under- 
stood ; as, not a man, which may imply any 
other being. 

Not Brutus, Incorporeal, Unfinished, Unwise. 



26 ELEMENTS OF LOGIC. 

12. A Definite Term is one which does de- 
fine or mark out an object and has not the 
particle not attached to it ; as, 

Man, Brutus, Finished, Complete, Established. 
EXAMPLES. 

1. Man is a rational being. 

2. Cicero was a great orator. 

3. This town is pleasantly situated. 

4. Mothers have much solicitude. 

5. Strength is acquired by exercise. 

6. Far-sightedness is peculiar to seamen. 

7. A dumb man is a pitiful object. 

8. The silent tomb, the lifeless statue. 

9. Wisdom is more precious than rubies. 

10. Just and good are the laws of God. 

11. The society is organized. 

12. The plan is incomplete. 



SECTION II. 

OPPOSITION OF TERMS. 

13. Consistent Teems are those which may 
at the same time be affirmed of the same thing ; 
as, dry and cold. 



OPPOSITION OF TEEMS. 27 

14. Opposite Terms cannot at the same time 
be affirmed of the same thing; as, black and 
white. 

The opposition of terms is fourfold. 

15. Relative Opposition is that which is be- 
tween relative terms, that cannot at the same 
time be applied to the same subject; as, father 
and son. 

16. Contrary Opposition is that between 
absolute terms, that expel one another from a 
subject capable of either ; as, wise and foolish. 

IT. Privative Opposition is that between a 
positive and privative term ; as, seeing and 
Hind. 

18. Contradictory Opposition is that be- 
tween a definite and indefinite term ; as Cesar 
and not Cesar. 



EXAMPLES. 

1. Good and small. 

2. Master and servant. 

3. Ruler and subject. 

4. Material and immaterial. 

5. Lovely and hateful. 

6. Hearing and deaf. 



28 ELEMENTS OF LOGIC. 

SECTION III. 

SPECIES AND GENUS. 

This subject involves no mystery, as formerly 
under a false philosophy. 

19. Species is a term that denotes a class, in- 
cluding several individuals ; as, Beast, which in- 
cludes the horse, cow, lion, deer, etc. 

20. Genus is a term that denotes a class, that 
includes several species ; as Animal, which in- 
cludes beast, bird, fish, man, insect. 

A genus which cannot be comprehended 
under a higher genus is called highest genus; 
and a species which includes no lower species 
is called lowest species. 

21. The Essential Difference denotes an 
essential part of a species that distinguishes it 
from other species ; as rational, which is the 
essential difference of the species man, because 
it is the essential part of man that distinguishes 
him from beast, bird, etc. 

22. A Property is something necessarily 
joined to the essential difference ; as power of 
laughing, which is the property of man as a 
rational being. 



SPECIES AND GENUS. 29 

18. An Accident is something that may be, 
i may not be joined to the essential difference, 
as tall or short, living in London, horn in 
Paris. 

EXAMPLES 

1. This tree is a Pine, with very thick 
boughs. 

2. This is a small magnet, having the power 
of attraction, and it turns upon a pivot in a 
direction north and south. 

3. This vessel is a ship, having three masts, 
full rigged, and very long. 

4. A republic is a government in which the 
people have sway and choose their own rulers. 

5. This seminary of learning is a college. 

6. A lame animal, a blind stag. 

7. General terms are names of classes. 

8. A bird with blue feathers and broad 
wings. 

9. Mercury is the planet nearest the Sun. 

10. A circle is a figure whose circumference 
is in every part equally distant from the 
center. 

11. A whale is the largest of fish, and is 
often seen in our waters. 



30 ELEMENTS OF LOGIC. 

12. A plant is an organized being, destitute 1 
of sensation. 



SECTION IY. 

DIVISION. 

24. Division is the distinct enumeration of 
the several things signified by a term ; as, 

New England is divided into Maine, New Hampshire, 
Vermont, Massachnsetts, Rhode Island, and Connecticut. 

Bark signifies the rind of a tree, a small ship, and the 
cry of a dog. 

25. Rule of Division. The several parts must 
not he contained in one another, and all to- 
gether must he exactly equal to the thing 
divided. 

EXAMPLES.* 

1. The year is divided into Summer, 
Autumn, Winter, and Spring. 

2. Metals are divided into gold, copper, and 
iron. 

3. The Human race is divided into Ameri- 
cans, Africans, Asiatics, Chinese, and Europeans. 

* Examples, it will be seen, are given for criticism. 



DEFINITION. 31 

4. King signifies a ruler and also a man's 
name. 

5. Mercury is the name of a heathen deity, 
a planet, a plant, and quicksilver. 

6. The globe consists of land and water. 

7. Form signifies shape and ceremony. 

8. Trump is a trumpet and a winning card. 

9. Orchard is an inclosure for apple-trees 
and fruit-trees. 

10. A solid body has length and breadth. 

11. A tree consists of trunk, branches, and 
leaves. 

SECTION" V. 

DEFINITION. 

26. A Definition is an expression explaining a 
term, so as to distinguish or separate it from 
everything else. 

27. A Nominal Definition distinguishes the 
meaning of a term by an equivalent term, 
which is better known ; as, 

Decalogue — the Ten Commandments. 

When all the equivalent terms are given it is 
one kind of division. 



32 ELEMENTS OF LOGIC. 

28. A Physical Definition lays down the 
real parts of the essence ; as, 

Injustice is the intentional violation of another's rights. 
A plant has leaves, stalks, roots. 

This last is another kind of division. 

29. A Logical Definition assigns the Genus 
and the Essential Difference of the thing de- 
fined; as, 

Man is a rational animal. 

30. Accidental Definition, or Description, 
assigns the accidents or properties of the thing 
defined ; as, 

Man is an animal that uses fire to dress his food. 
Columbus was a native of Genoa. 

31. It will be observed that more than one 
of these kinds of definition will coincide in 
matters strictly scientific. 

32. Rule of Definition. A Definition must 
be adequate, that is, not too extensive nor too 
narrow, for the tiling defined j plainer, and 
contained in a suitable number of proper, not 
figurative terms. 

-33. The chief concern of Logic with defini- 



DEFINITIONS. 33 

! 

! tions is, that words be not used in different 
\ senses in argument. 

EXAMPLES. 

1. Pleiades — the seven stars. 

2. A king is the ruler of a people. 

3. A square is a figure having four sides and 
four right angles. 

4. Surprise is a state of mind produced by 
some unexpected occurrence. 

5. A circle is a figure whose circumference 
is in every point equally distant from the 
center. 

6. Species is a term for a class. 

7. "Wine is the juice of the grape. 

8. "Whiteness is the color arising from the 
prevalence of brightness. 

9. A plant is an organized being destitute of 
sensation. 

10. Logic is the science of inference. 

11. Man is a risible animal. 

12. Mercury is the planet nearest the Sun. 

13. A Church is a congregation of faithful 

men, in which the word of God is preached, 

and the ordinances duly administered. 
3 



34 ELEMENTS OF LOGIC. 

14. Punishment is pain inflicted for a crime, 
in order to correct the offender. 

15. Courage is boldness and endurance in 
time of peril. 

16. Sin is voluntary transgression of a known 
law. 

17. Sin is any transgression of God's law. 



PART II. 



OF PROPOSITIONS. 

The second part of Logic treats of Propo- 
sitions. 

SECTION I. 

1. A Proposition is a judgment expressed 
in words, or a sentence, whereof one part 
is affirmed or denied of the other ; as, 

Man is an animal. 

Moses and Thomas are not Statesmen. 

All animals are mortal. 

2. The Subject of a proposition is that part, 
of which something is affirmed or denied ; as, 
in the last example all animals is the subject. 

3. The Predicate of a proposition is that 
which is affirmed or denied of the subject; as, 
in the same example, mortal is the predicate. 



36 ELEMENTS OF LOGIC. 

4. The Copula is the verb by which the 
two terms are connected. It is the present tense 
of the verb to be, with or without the particle not 

5. Sometimes one part of a proposition is 
contained , in another ; as, the wind blows, I 
think; which imply, I am thinking, the wind is 



6. The subject of a proposition usually 
stands first, and the predicate last; but this 
order is sometimes inverted, as, 

In the "West are extensive Prairies. 

EXAMPLES. 

1. Matter is divisible. 

2. Man is not infallible. 

3. Christopher Columbus was the discoverer 

of America. 

4. A wise man rules his own spirit. 

5. George Washington was a brave but pru- 

dent general. 

6. The world exhibits marks of a great con- 

vulsion. 

7. I see — he feels — you walk — they run. 

8. All tyrants deserve death. 

9. Blessed are the pure in heart. 



DISTINCTION OF PEOPOSITIONS. 37 

SECTION II. 

DISTINCTION OF PEOPOSITIONS. 

7. Propositions are distinguished into af- 
firmative and negative, which is a distinction 
with respect to Quality. 

8. An Affirmative Proposition is one in 
which the predicate is declared to agree with 
the subject ; as, 

Man is a fallible creature. 

9. A Negative Proposition is one in which 
the predicate is declared to disagree with the 
subject; as, 

The world is not eternal ; no miser is happy. 

10. Propositions are also distingnished into 
Universal and Particular, which is a distinc- 
tion in respect to Quantity. 

11. A Universal Proposition is one in which 
the predicate is asserted of the whole of the 
subject. 

The signs of universality are all, every, no, 
neither, and the like, which are expressed or 



38 ELEMENTS OF LOGIC. 

understood ; also, proper names, as John, Lon- 
don; and common names with a singular or 
a definite sign ; as, That hoy, five hooks. 

No discontented man is happy. • 

Those stars revolve about the sun. 

Exceptions. In negative propositions the 
idiom of the English language makes all and 
every particular or singular terms ; as, all the 
sailors were not drowned, does not mean that all 
the sailors escaped drowning, but that some of 
them only escaped drowning ; or, it denies 
drowning of the totality as a collective unit. 

To. state a universality here you must say : 
None of the sailors were drowned, or simply, 
The sailors were not drowned. 

12. A Particular Proposition is one in 
which the predicate is asserted of an indefinite 
part of the subject. 

The signs of particularity are some, many, 
few, several, and the like ; as, 

Some culprits were not punished. 

13. A Universal Affirmative Proposition 
is one in which the predicate is said to agree 



DISTINCTION OF PROPOSITIONS. 39 

with the whole of the subject ; as, in the above 
example — All men are mortal. This is not only 
a universal proposition, but a universal affirma- 
tive proposition. 

All tyrants deserve death. 

14. A Universal Negative Proposition is 
one in which the predicate is said to disagree 
with the whole of the subject; as, no discon- 
tented man is happy; which is not only a uni- 
versal proposition, but a universal negative 
proposition. 

No sins are excusable. 

15. A Particular Affirmative Proposition 
is one in which the predicate is asserted to 
agree with only some part of the subject; as, some 
islands are fertile; which is not only a par- 
ticular proposition, but a particular affirmative 
proposition. 

Several men were drowned. 

16. A Particular Negat^e Proposition is 
one in which the predicate is asserted to dis- 
agree with only some part of the subject ; as, some 
culprits were not punished; which is not only 



40 ELEMENTS OF LOGIC. 

a particular proposition, but a particular nega- 
tive proposition. 

17. A, E, I, O are symbols employed to re- 
present these propositions : thus, 

A stands for universal affirmative. 

E stands for universal negative. 

I stands for particular affirmative. 

O stands for particular negative. 

EXAMPLES. 

1. These sailors were not drowned. 

2. Paris is a gay city. 

3. Some animals are sagacious. 

4. Men are unaccountable beings. 

5. Every effect must have an adequate 

cause. 

6. Few men become suddenly rich. 

7. Many criminals are not brought to pun- 

ishment. 

8. Planets are bodies moving in orbits about 

the sun. 

9. Islands are surrounded by water. 

10. The Christian religion is attested by 

miracles. 

11. Every sinner will be punished. 



DISTINCTIONS OF PROPOSITIONS. 41 

12. That man was the inventor of lightning 

rods. 

13. Not all his foes could alarm him. 

14. No flower, is always in bloom. 

15. All laws are not useful. 

16. Every soldier was not killed. 



SECTION III. 

FURTHER DISTINCTIONS OF PROPOSITIONS. 

18. Propositions are distinguished into Cate- 
gorical and Hypothetical. 

19. The Categorical asserts simply that the 
predicate agrees or disagrees with the sub- 
ject; as, 

Truth is invaluable. 

The eye is a natural telescope. 

20. The Hypothetical asserts with a con- 
dition, or with an alternative ; as, 

If It storms, the ship will not sail. 
It is summer or winter. 

21. Hypothetical Propositions are divided 
into Conditional and Disjunctive. 



42 ELEMENTS OF LOGIC. 

22. A Conditional Proposition is one whose 
parts are limited by the particle if, or some 
word expressing a condition ; as, 

If there be no fire, there will be no heat, 
Cesar deserved death, if he was a tyrant. 

23. A Conditional Proposition contains two, 
and only two, Categorical Propositions, whereof 
one follows from the other. 

If the Bible is true, it ought to be studied. 

The first is called the antecedent, and that 
which results from it is called the consequent. 

24. A Disjunctive Proposition asserts that 
a subject agrees with one of two or more pred- 
icates, or a predicate with one of two or more 
subjects; as, 

It is either day or night. 

Prosperity or adversity will be your lot. 

25. A Disjunctive may easily be converted 
into a Conditional ; thus, 

It is either day or night. 
If it is not day, it is night. 



TEEMS OF PROPOSITIONS. 43 

EXAMPLES. 

1. Man is free, or he is not responsible. 

2. This proposition is either true or false. 

3. The earth must move, if the sun be fixed. 

4. If the harvest is large, corn will be cheap. 

5. If there be no providence, prayer avails not. 

6. If the boat goes, the letter will probably 

reach him before morning. 

7. Wisdom is the principal thing, if Solomon 

is right. 

8. Either the sun or the moon will be eclipsed 

that day. 

9. If logic is useful, it deserves to be studied. 
10. If Cromwell was an Englishman, he was 

a usurper. 

SECTION IV. 

DISTRIBUTION OF THE TERMS OF PROPOSI- 
TIONS. 

26. A Term is said to be distributed when it 
is taken universally or in its utmost extent, so 
as to stand for everything to which it is capable 
of being applied, that is, for each of its signifi- 
cates ; and undistributed when it stands for an 



44 ELEMENTS OF LOGIC. 

indefinite portion only of the things signified 
by it, that is, for an indefinite part of a class. 
In the following example the subject is dis- 
tributed and the predicate undistributed. 

All birds are animals. 

In the following the predicate is distributed 
and the subject undistributed. 

Some birds are not web-footed. 

[ 
It is evident that the whole class of web- 
footed are separated by the not from some 
birds. 

RULE I. 

27. /Subjects are distributed in all universal 
and no particular propositions. 

All men are mortal. 
Great Britain rules the ocean. 
"Wicked men are not wise. 
The fixed stars twinkle. 
No miser is a happy man. 

RULE n. 

28. Predicates are distributed in all negative 
and no affirmative propositions. 

Ho virtue is an evil. 

Some rich men are not good men. 



TERMS OF PROPOSITIONS. 45 

A distributes the subject, O the predicate, I 
peither, and E both. 

E". B. — A definite portion of a class is a small 
class, and the term which expresses it is dis- 
tributed. 

Most men are poor. 
These men are rich. 

Rule II has some Exceptions in what logi- 
cians call unnatural- propositions, such as, 

All triangles are all figures bounded by three straight 
lines. 
Some stars are all the planets. 
Some stars are not some planets. 

But these being noted by the form of ex- 
pression will make no difficulty. 

I do not see with Sir William Hamilton suffi- 
cient reason, in such exceptions, to revolutionize 
the established forms of logic. 

EXAMPLES. 

1. Many ships were lost in the gale. 

2. The storm did not last long. 

3. Most Americans can read. 

4. All the laws were not enforced. 



46 ELEMENTS OF LOGIC. 

5. Everything in the political world looks 

dark. 

6. 'No good man can hate his brother. 

7. Every sin is a violation of the divine law. 

8. All visible things had a beginning. 

9. Some difficult things are not evils. 

10. Charity never faileth. 

11. Charity suffereth long and is kind. 

12. Five men were shipwrecked. 

SECTION V. 

OPPOSITION" OF PKOPOSITIONS. 

29. Two propositions are said to be opposed, 
which, having the same subject and predicate, 
yet differ in quantity, or quality, or both ; as, 

A. All islands are fertile, ) . 

T « . ■. -. ,. , ., r m quantity. 

I. Some islands are fertile, ) 

A. All islands are fertile, ) . 
E. No island is fertile, ) 

A. All islands are fertile, ) . 

0. Some islands are not fertile, ) 

E. No island is fertile, ) . 

1. Some islands are fertile, ) 






OPPOSITION OF PROPOSITIONS. 47 

30. With any given subject and predicate, 
four distinct propositions may be stated, namely, 
A, E, I, and O, any two of which may be said 
to be opposed ; as, 

A. Every disease is contagious. 
E. No disease is contagious. 



Or, 



I. Some diseases are contagious. 
O. Some diseases are not contagious. 



31. There are four different kinds of opposi- 
tion. 

32. Contrary Opposition is when a uni- 
versal affirmative is opposed to a universal 
negative ; as, 

A. All human inventions are perfect, 
E. No human invention is perfect. 

33. Subcontrary Opposition is when the 
particular affirmative is opposed to the particu- 
lar negative ; as, 

I. Some human inventions are perfect. 
O. Some human inventions are not perfect. 

34. Subaltern Opposition is when a univers- 
al affirmative is opposed to a particular affirm- 



48 ELEMENTS OF LOGIC. 

ative, or a universal negative to a particular 
negative; as, 

A. Every human invention is perfect. 
I. Some human inventions are perfect. 
Or, 

E. No human invention is perfect. 

O. Some human inventions are not perfect. 

35. Contradictory Opposition is when the 
universal affirmative and the particular negative 
are opposed, or the universal negative and the 
particular affirmative ; as, 

A. Every human invention is perfect. 

0. Some human inventions are not perfect. 

Or, 

E. No human invention is perfect. 

1. Some human inventions are perfect. 

36. Four conditions are requisite to consti- 
tute a contradiction, namely, to speak of the 
same thing : (1.) In the same sense ; (2.) In the 
same respect; (3.) With regard to the same 
third thing; and, (4.) At the same time. If any 
of these be wanting, is and is not may 
agree. As, 



OPPOSITION OF PROPOSITIONS. 49 

1. An opinion is and is not faith. It is an 
inoperative and unacceptable belief; it is not 
an effectual and saving faith. 2. Troilus is 
cmd is not red-haired. He is with respect to 
his head ; he is not with respect to his beard. 
3. Socrates is and is not long-haired, he is in 
comparison with Scipio ; he is not in compari- 
son with Xenophon. A. Solomon was and was 
not a good man. He was in his youth ; he was 
not in his middle age. 

THE KULES OF OPPOSITION. 
RULE I. 

37. Contradictory Propositions are always 
the one true and the other false ; as, 

A. All men are mortal. 

0. Some men are not mortal. 

E. No tyrant deserves death. 

1. Some tyrants deserve death. 

RULE II. 

38. Contrary Propositions may be both 

, but never both true ; as, 
4 



50 ELEMENTS OF LOGIC. 

A. Every disease is contagious. 
E. No disease is contagions. 

RULE m. 

39. Subcontraries are never both false, but 
they may be both true. 

I. Some amusements are innocent. 
O. Some amusements are not innocent. 

RULE IV. 

40. Subalterns are sometimes both true, 
sometimes both false, and sometimes one is true 
and the other false ; as, 

A. Every defensive war is just. 
I. Some defensive wars are just. 
E. No crime is an evil. 

0. Some crimes are not an evil. 

A. Every measure of government is wise. 

1. Some measures of government are wise. 

A^- Contraries E 

Diagram showing the \ / 1 

relation of the four judg- © %<^ g* 

ments: A E I O. 4 / 

-Subcontraries- 



OPPOSITIOX OF PROPOSITIONS. 51 

EXAMPLES. 

1. Some horses are unruly. 
Some horses are not unruly. 

2. No intolerant men are good men. 
Some intolerant men are good men. 

3. All pleasures are hurtful. 
Some pleasures are not hurtful. 

4. All hopes are consoling. 
Some hopes are consoling. 

5. E"o virtuous man is ungrateful. 
Some virtuous men are ungrateful. 

6. All islands are fertile. 
Some islands are fertile. 

7. All animals are mortal. 
All animals are not mortal. 

8. Every patriot is a Christian. 
Some patriots are not Christians. 

9. Some diseases are contagious. 
All diseases are contagious. 

tO. All laws are not useful. 
Some laws are not useful. 



52 ELEMENTS OF LOGIC. 

SECTION VI. 

CONVERSION OF PROPOSITIONS. 

41. A proposition is said to be converted, 
when its terms are transposed and the truth 
preserved; as, 

Some painters are poets. 
Some poets are painters. 

42. The proposition to be converted is called 
the Original, that into which it is converted 
the Converse ; as, 

Original. No reptile is a quadruped. 
Converse. No quadruped is a reptile. 

43. Simple Conversion is where the subject 
and predicate simply change places ; as, 

Some boasters are cowards. 
Some cowards are boasters. 

44. Particular Conversion is where, in 
transposition, the converse requires a particular 
term to preserve the truth of the original ; as, 



All swallows are birds. 
Some birds are swallows. 






CONVERSION OF PROPOSITIONS. 53 

45. Rule. In all cases the converse must he 
truly implied by the original, and no term 
must be distributed in the converse that was not 
distributed in the original. Hence, 

A. All men are mortal ; 
All mortals are men, 

is not proper conversion, for A distributes the 
subject only, (28) but mortal is the predicate, 
therefore its distribution in the converse, 
namely, all mortals, is unwarranted. 

46. The converse of a universal affirmative 
proposition is a particular affirmative ; or, more 
briefly, A is converted into I. 

A. All men are mortal. 
I. Some mortals are men. 

47. The converse of a universal negative is a 
universal negative — E into E ; as, 

E. No deer is an elephant. 
E. No elephant is a deer. 

48. Particular affirmative propositions are 
converted only into the same — I into I ; as, 

I. Some infidels are learned men. 
I. Some learned men are infidels. 



54 ELEMENTS OF LOGIC. 

49. A particular negative is inconverti- 
ble; as, 

O. Some birds are not swallows. 

You cannot say, 

0. Some swallows are not birds ; 
Or, 

E. No swallows are birds ; 

For these are negative propositions, and dis- 
tribute the predicate, (28) which is birds; but, 
in the original, fords, is not distributed. (27.) 

Some logicians teach that the particular 
negative may be converted by considering the 
particle not attached to the predicate, by which 
the proposition is taken as an affirmative. 

Some statesmen are not wise, may be stated : 

Some statesmen are not- wise. 
This you may convert simply: 

Some not- wise, that is, nnwise, are statesmen. 



In like manner a universal affirmative may 
be simply converted by changing its quality ; 

thus, 

All good reason ers are candid men, 

may be converted into 

None but candid men are good reasoners. 






CONVERSION OF PROPOSITIONS. 55 

This is called conversion by contraposition. 

50. Exceptions. Universal affirmatives may 
be converted simply when the predicate by 
some word notifies its distribution, contrary to 
rule, sec. iv, 28, and when it is understood to be 
exactly equal to the subject, as in definitions, 

etc. 

All men are [all] rational animals. 

So some particular negative proposition may 
be converted simply when the predicate notifies 
its non-distribution. See exceptions to Rule II, 

Sec. iv, 28. 

Some elms are not some trees. 
EXAMPLES. 

1. All Britons are freemen. 

2. Some Britons are freemen. 

3. No unhappy man is a perfect Christian. 

4. Some fish are not salmon. 

5. Some orators are not statesmen. 

6. No offensive wars are righteous enter- 

prises. 

7. Every learned man is a thankful man. 

8. Some great geniuses are ignorant men. 

9. Some parrots are not talkers. 



56 ELEMENTS OF LOGIC. 

10. Every true Christian is a patriot. 

11. Some angels are sinners. 

12. Some amusements are hurtful. 

13. All birds have feathers and wings. 

14. All equiangular triangles are equilateral. 

15. Some stars are all the planets. 

16. Some stars are not some planets. 

17. A few men are not all the voters. 

18. Some birds are not like some birds. 






PART III. 



OF AEGUMElsTT. 

1. The third part of Logic treats of Argu- 
ment, or reasoning expressed in words. 

2. An Argument is an expression in which, 
from something laid down and granted as true, 
something else beyond this must be admitted to 
be true, as following necessarily from the other. 
That which is laid down is called the Premises, 
that which results therefrom is called the Con- 
clusion. 

3. Every valid argument must conform to 
the Logical axiom, that being the only prin- 
ciple on which all reasoning proceeds, namely : 
Whatever is universally affirmed or denied of a 
class, may he affirmed or denied, in like manner, 
of everything comprehended in that class. 

Or, as stated by Aristotle, and hence called 
Aristotle's dictum : 



58 ELEMENTS OF LOGIC. 

WJiatever is predicated of a term distributed 
may be predicated in like manner of eve 
thing contained in it. As, 

All tyrants deserve death ; 

Cesar was a tyrant ; 

Therefore Cesar deserved death. 

No man enslaved by appetite can be happy ; 
The sensualist is enslaved by appetite ; 
Therefore, no sensualist can be happy. 



SECTION I. 

OF SYLLOGISM. 

4. An argument stated at full length and in 
its regular form is a Syllogism. The above 
examples are syllogisms. 

5. Every regular syllogism contains three, 
and only three terms, called the Minor term, 
Major term, and Middle term. 

All tyrants deserve death. 
3 2 

Cesar was a tyrant, 

1 3 

Therefore, Cesar deserved death. 
l 2 



OF SYLLOGISM. 59 

6. The subject of the conclusion is the minor 
term; the predicate of the conclusion is the 
major term ; and the other term with which 
these are compared is the middle term ; as, 

All tyrants deserve death ; 

Middle. 
Cesar was a tyrant ; 

Minor. Mayor. 

Therefore Cesar deserved death. 

The predicate of the conclusion is called the 
major term on account of its being naturally 
more extensive than the subject. By the 
rule it is undistributed in affirmative proposi- 
tions, that is, it has applications beyond the 
subject. Part II, Sec. iv, 28. 

In the example, deserving death is applicable 
to many besides Cesar. 

7. Every regular syllogism contains three, 
and only three propositions, called the Major 
premise, the Minor premise, and the Conclu- 
sion. 

8. The Major Premise is that in which the 
major term is compared with the middle term. 

Major Premise. All tyrants deserve death; 
Cesar was a tyrant; 
Therefore, Cesar deserved death. 



60 ELEMENTS OF LOGIC. 

9. The Minor Premise is that in which the 
minor term is compared with the middle 
term; as, 

All tyrants deserve death ; 
Minor Premise. Cesar was a tyrant ; 

Therefore, Cesar deserved death. 

10. The Conclusion is that in which the 
major and the minor terms are compared to- 
gether. 

All tyrants deserve death ; 
Cesar was a tyrant ; 
Conclusion. Therefore, Cesar deserved death. 

11. In every regular syllogism the major 
premise is placed first, the minor next, and the 
conclusion last. 

EXAMPLES. 

1. All the faithful are dear to God ; 
Some that are afflicted are faithful ; 
Therefore, some that are afflicted are dear 

to God. 

2. No work that exhibits marks of design 

can be the effect of chance ; 
The world exhibits marks of design, 
Therefore, the world cannot be the effect 

of chance. 



THE RULES OF SYLLOGISM. 61 

3. That which improves the mind is useful ; 
Study improves the mind ; 
Therefore, study is useful. 

4. No literary production is perfect. 
This treatise is a literary production ; 
Therefore, this treatise is not perfect. 

5. Every vegetable is combustible ; 
Every tree is a vegetable ; 
Therefore, every tree is combustible. 

SECTION II. 

THE EULES OF SYLLOGISM. 

12. The validity of all arguments may be 
tested by the logical axiom (3) ; and no syllo- 
gism is valid which does not conform to it. 

13. It cannot, however, always be directly 
and conveniently applied; as, for example, in 
the following valid syllogism : 

No virtues are evils ; 

All virtues are difficult ; therefore, 

Some difficult things are not evils. 

This syllogism may be altered by converting 
the minor premise, and then it will plainly 
appear to conform to the logical axiom; thus, 



62 ELEMENTS OF LOGIC. 

No virtues are evils ; 

Some difficult things are virtues ; therefore, 

Some difficult things are not evils. 

14. But to avoid the inconvenience of alter- 
ing a syllogism, in order to apply the logical 
axiom, logicians have adopted the following 
canons and rules by which to test the validity 
of syllogisms. 

15. Canon I. If two terms agree with one 
and the same third, they agree with each other. 

16. Canon II. If one term agrees and the 
other disagrees with one and the same third, 
these two disagree with each other. 

This agreement must be understood to be 
that kind of class relation explained by the 
logical axiom, and required by Aristotle's 
dictum, otherwise the canons will mislead. 

Silver is a mineral ; 
Platina is a mineral ; 

Will not prove that platina is silver, though 
these terms agree with the term mineral. 

All studies which tend to increase national and private 
wealth are useful ; 

The studies at Oxford do not tend to increase national 
and private wealth ; 

Therefore, the studies at Oxford are not useful. 



THE RULES OF SYLLOGISM. 63 

# 

This might at first seem to be founded on 
canon II, but it is a fallacy, as is easily seen in 
a case precisely parallel. 

All cultivated plants grow ; 

The wild rose-bush is not cultivated ; 

Therefore, the wild rose-bush does not grow. 

John Jones is sentenced to die ; 

The first private in the ranks is John Jones ; 

Therefore, the first private in the ranks is sentenced to die. 

Here the first canon is observed, but the 
logical axiom is not complied with unless you 
consider proper names as distributed and stand- 
ing for a class of one. See Part II, Sec. ii, 11 ; 
and Sec. iv, 28. Strictly this is rather a case 
of identification than of inference. 

To avoid error, we must add to the two 
canons the following six rules or cautions : 

RULE I. 

17. Every syllogism must have three, and 
only three terms, and three, and only three, 
propositions. 

Ambiguous terms are to be considered as 
two terms. 



64 ELEMENTS OF LOGIC. 

The following example has, in reality, four 
terms : 

Repentance is a good thing ; 
"Wicked men abound in repentance ; 
Therefore, wicked men abound in a good thing. 

If the word repentance be regarded as having 
the same meaning in both premises, then one 
proposition or the other is false. 

Ambiguous terms are fruitful sources of error 
in argument. 

Sometimes an argument will appear to 
have too many terms when a little alteration, 
not affecting the sense, will show but three ; 
thus : 

No irrational agent could produce a work which manifests 

design ; 
The universe is a work which manifests design ; 
Therefore, no irrational agent could have here produced 

the universe; 

This seems to have five terms, but the first pre- 
mise is properly: 

A work that manifests design could not be produced by 
an irrational agent. 



THE RULES OF SYLLOGISM. 65 

RULE II. 

18. The middle term must he distributed once 
at least in the premises. 
The following example violates the rule : 

Granite is a mineral ; 
Lead is a mineral ; 
Therefore, lead is granite. 

The middle term mineral is undistributed; 
hence, granite is compared to mineral in a 
part of its extension, and lead is compared to 
it in another part of its extension ; therefore, 
neither of the canons of logic are complied 
with, for the two extremes are not compared 
to one and the same third. 

The following seems to violate the rule: 

True patriots are disinterested ; 
Few men are disinterested ; 
Therefore, few men are true patriots. 

But by putting the minor premise in another 
form, and transposing the premises, it would 
stand thus: 

Disinterested men are few ; 
True patriots are disinterested ; 
Therefore, true patriots are few. 



66 ELEMENTS OF LOGIC. 

RULE III. 

19. No term must be distributed in the con- 
clusion, which was not distributed in one of the 
premises. 

The following violates the rule: 

Some diseases are contagious ; 

No rheumatic fevers are contagious ; 

Therefore, rheumatic fevers are not diseases. 

Here you employ the term diseases in the 
whole of its extent in the conclusion, while you 
employ it in only a part of its extent in the 
premise. 

RULE IV. 

20. Two negative or two particular premises 
prove nothing. As, 

Slate is not a metal. 
Flint is not a metal. 

Here two terms disagree with a third. This 
is not according to the canons, which requires 
either that both should agree with the third, or 
one agree and the other disagree. 

Some bad men are eloquent orators ; 
Some good men are eloquent orators ; 
Therefore, some good men are bad men. 



THE RULES OF SYLLOGISM. 67 

Here you have the middle term undis- 
tributed, which is contrary to Rule 2, and 
therefore, not according to the canons. 

Some bad men are eloquent orators ; 
Some good men are not eloquent orators ; 
Therefore, some good men are not bad men. 

This is contrary to Rule 3. 

The following syllogism with negative 
premises may be made regular by considering 
one of them an affirmative : 

No man is happy who is not secure ; 
No tyrant is secure ; 
Therefore, no tyrant is happy. 

No man who is insecure is happy ; 
Every tyrant is insecure; 
Therefore, no tyrant is happy. 

RULE V. 

21. If either premise he negative or particu- 
lar, so also is the conclusion. As, 

No virtuous man is a rebel ; 
X and Y are virtuous men ; 
Therefore, X and Y are not rebels. 



68 ELEMENTS OF LOGIC. 

Here one term is said to disagree with a 
middle and the other to agree, hence they dis- 
agree with each other, and the conclusion 
must be negative. 

All who study diligently deserve reward ; 
Some scholars study diligently ; 
Therefore, some scholars deserve reward. 

Here is a particular premise, and you cannot 
draw anything but a particular conclusion, for 
a universal conclusion would be contrary to 
Rule 3, and against the canons. 

The following in form violates the first part 
of this rule, but it might be stated so as to be ( 
regular. 

None but candid men are good reasoners. 

Few infidels are candid ; 

Therefore, few infidels are good reasoners. 

It may be changed thus : 

All good reasoners are candid ; 

Most infidels are not candid ; 

Therefore, most infidels are not good reasoners. 

Or thus : 

Those who are uncandid are not good reasoners; 

Most infidels are uncandid; 

Therefore, most infidels are not good reasoners. 



THE RULES OF SYLLOGISM. 69 

EXAMPLES. 

1. No one is free who is enslaved by his ap- 

petites ; 
A sensualist is enslaved by his appetites ; . 
Therefore, a sensualist is not free. 

2. All gold is precious ; 
This mineral is precious ; 
Therefore, this mineral is gold. 

3. All wise legislators adapt their laws to the 

genius of the people ; 
Solon adapted his laws to the genius of the 

people ; 
Therefore, Solon was a wise legislator. 

4. All pious men desire the freedom of their 

country ; 
Thomas Paine desired the freedom of his 

country ; 
Therefore, Thomas Paine was a pious man. 

5. Warm countries alone produce wine ; 
Spain is a warm country ; 
Therefore, Spain produces wine. 

6. Some poisons are vegetables ; 
No poisons are useful drugs ; 
Therefore, some useful drugs are not vege- 
tables. 



70 ELEMENTS OF LOGIC. 

7. They who subvert the foundations of mo 

rality ought not to be respected ; 
Atheists subvert the foundations of mo 

rality ; 
Therefore, Atheists ought not to be re 

spected. 

8. All vegetables grow; 
This animal grows; 

Therefore, this animal is a vegetable. 

9. Most men are poor ; 
Most men are intelligent ; 

Therefore, some intelligent men are poor. 

10. Light is contrary to darkness ; 
Feathers are light ; 

Therefore, feathers are contrary to dark- 
ness. 

11. An enslaved people is not happy ; 

The English are not an enslaved people ; 
Therefore, the English are happy. 

12. None but whites are civilized ; 
The Ancient Germans were whites; 
Therefore, they were civilized. 

13. None but whites are civilized ; 
The Hindoos are not whites ; 
Therefore, they are not civilized. 



IRREGULAR SYLLOGISMS. 71 

14. .None but civilized people are white ; 
The Gauls were white ; 
Therefore, the Gauls were civilized. 



SECTION III. 

IRREGULAR SYLLOGISMS. 

22. The Enthymeme is a defective syllog- 
ism, having one premise suppressed ; as, 

Christianity teaches the way to future happiness ; 
Therefore, it should be diligently sought. 

Here the major premise is suppressed. Sup- 
ply it, and the syllogism is complete ; thus, 

Whatever teaches the way to future happiness should 
be diligently sought ; 
Christianity teaches the way to future happiness ; 
Therefore, Christianity should be diligently sought. 

Every man is mortal ; 
Therefore, every king is mortal. 

Here the minor premise is omitted. (9.) 
Frequently the conclusion is stated first; 
thus, 

Enthusiasm should be avoided, 
Because it leads astray from reason. 



72 ELEMENTS OF LOGIC. 

23. A regular syllogism may be changed 
into an Enthymeme by simply suppressing one 
of the premises, or by stating the conclusion 
first, and joining thereto one of the premises by 
the conjunction for, as, or because. As, 

Whatever enables us to overcome difficulties is useful , 
Perseverance enables us to overcome difficulties ; 
Therefore, perseverance is useful. 

This may be changed to Enthymeme, thus : 

Whatever enables us to overcome difficulties is useful ; 
Therefore, perseverance is useful. 

Or thus : 

Perseverance enables us to overcome difficulties ; 
Therefore, perseverance is useful. 

Or thus : 

Perseverance is useful, for it enables us to overcome 
difficulties. 

Or thus : 

Perseverance is useful ; for, 

Whatever enables us to overcome difficulties is useful. 

24. To reduce an Enthymeme to a syllogism, 
observe first what is the conclusion or point 



IRREGULAR SYLLOGISMS. 73 

established. This contains the minor and major 
terms, (10) and the remaining term must be the 
middle term. Having these, the syllogism may 
be easily constructed according to the rules 
(Sec. I.) by supplying the implied premise. 

In the last example," perseverance is useful, is 
j the conclusion. Consequently the remaining 
term, enables us to overcome difficulties, is the 
middle term. (6.) Perseverance enables us to 
overcome difficulties is implied, and makes the 
minor premise. (9.) 

25. The Sorites is a continued argument, 
consisting of a series of propositions arranged 
in such a manner that the predicate of each 
forms the subject of the following proposition, 
except the concluding, which takes the subject 
of the first proposition ; as, 

There can be no enjoyment of property without gov- 
ernment ; 

No government without laws enforced ; 

No laws enforced without a magistrate ; 

No magistrate without obedience; 

And no obedience where every one acts as he pleases ; 
therefore, 

There can be no enjoyment of property where every- 
one acts as he pleases. 



74 ELEMENTS OF LOGIC. 

26. Every Sorites contains as many syllo- 
gisms as there are propositions intervening 
between the first and the last proposition. 

The English are a brave people ; 
A "brave people are free; 
A free people are happy ; 
Therefore, the English are happy. 

This may be broken up into two syllogisms, thus : 

A brave people are free ; 

The English are a brave people ; 

Therefore, the English are free. 

A free people are happy ; 
The English are a free people ; 
Therefore, the English are happy. 

27. The Epicherema is a compound -argu- 
ment, of which one or both the premises are 
separately proved before the conclusion is 
drawn. As, 

Unjust laws endanger the stability of government, for 
they create discontent among the people; 

Laws restraining freedom of eonscience are nnjnst, for 
they require the people to abandon their dearest concerns; 

Therefore, laws restraining freedom of conscience en- 
danger the stability of government. 



IRREGULAR SYLLOGISMS. 75 

28. Irregular syllogisms are the most com- 
monly employed in discourses of every kind; 
for the regular form of syllogism would not 
often consist with elegance of style, nor is it 
often requisite to produce conviction. 

EXAMPLES. 

1. The mind is a thinking substance ; 
A thinking substance is a spirit ; 

A spirit has no composition of parts ; 
That which has no composition of parts 

is indissoluble ; 
That which is indissoluble is immortal ; 
Therefore, the mind is immortal. 

2. He is a good man, therefore he is happy. 

3. He is a miserable man, because he is 

vicious, 

4. Whatever tends to subvert government 

should be deprecated ; 
Therefore, civil dissensions should be dep- 
recated. 

5. Every man is an animal ; 

Every animal is a living creature ; 
Every living creature is a substance ; 
Therefore, every man is a substance. 



76 ELEMENTS OF LOGIC. 

6. A religion attested by miracles is from God, 

for none but God can suspend the laws 
of nature, and God would not permit 
them to be suspended but for his glory. 
The Christian religion was attested by 
miracles, for the friends and the enemies 
of Christianity have agreed in declaring 
it was; 
. Therefore, the Christian religion is from 
God. 

7. No opinion that tends to immorality should 

be embraced. 
Atheistical sentiments tend to immo- 
rality ; 
Therefore, atheistical sentiments should 
not be embraced. 

8. It is lawful for one man to kill another 

who lies in wait to kill him, for the laws 

of nature and the customs of mankind 

sanction it ; 
Clodius lay in wait to kill Milo, for his 

equipage, arms, guards, movements, 

etc., prove it ; 
Therefore, it was lawful for Milo to kill 

Clodius. 






HYPOTHETICAL SYLLOGISMS. 77 

9. With some of them God was not well 
pleased, for they were overthrown in the 
wilderness. 

10. He that is of God heareth my words; 

ye therefore hear them not, because ye 
are not of God. 

11. Men are free agents, for they are account- 

able beings. 

12. Skepticism is an enemy to man, since it is 

an enemy to truth. 

SECTION IY. 

HYPOTHETICAL SYLLOGISMS DILEMMA. 

Hypothetical Syllogisms are of two kinds: 
Conditional and Disjunctive. 

29. A Conditional Syllogism is one in which 
the major premise is a conditional proposition ; 
as, 

If there is a God, this world is governed by a provi- 
dence ; 

But there is a God ; 

Therefore, this world is governed by a providence. 

30. The clause containing the condition is 
called the Antecedent, that containing the as- 
sertion is called the Consequent. 



78 ELEMENTS OF LOGIC. 

31. Rule. If the antecedent "be granted so is 
the consequent, if the consequent be denied so is 
the antecedent * but not vice versa/ that is, the 
antecedent being denied proves nothing, and the 
consequent being granted, proves nothing ; as, 

If Samuel is a father he has authority; 
But Samuel is a father ; 
Therefore, he has authority. 

If Samuel is a father he has authority ; 
But he has not authority ; 
Therefore he is not a father. 

But vice versa, the argument is not valid. 

If Samuel is a father he has authority ; 
But Samuel is not a father ; 
Therefore, he has not authority. 

But he might have authority from some other 
relation or office. Again, 

If Samuel is a father he has authority ; 
But he has authority ; 
Therefore, he is a father. 

32. Conditional Syllogisms may be reduced to 
regular syllogisms, by considering the anteced- 
ent the subject, and the consequent the predicate 
of an universal affirmative proposition. 



HYPOTHETICAL SYLLOGISMS. 79 

If the Atheists are right the world exists without a 
cause ; 
But the Atheists are not right ; 
Therefore, the world does not exist without a cause. 

Reduced thus, when it appears a fallacy : 

The case of the Atheists being right is the case of the 
world existing without a cause ; 

But the present case is not the case of the Atheist being 
right ; 

Therefore, the present case is not the case of the world 
existing without a cause. (See Kule 3, Sec. ii.) 

33. A Disjunctive Syllogism is one whose 
major premise is a disjunctive proposition. 

The earth either moves in a circle or an ellipse. 
But the earth does not move in a circle ; 
Therefore, it moves in an ellipse. 

It is either spring, summer, autumn, or winter; 
But it is not summer, autumn, or winter ; 
Therefore, it is spring. 

34. Disjunctive syllogisms are easily con- 
| vertible into conditional, and so brought under 
I the foregoing rules ; as, 



80 ELEMENTS OF LOGIC. 

If the earth does not move in a circle it moves in an 
ellipse ; 
But it does not move in a circle ; 
Therefore, it moves in an ellipse. 

35. The Dilemma is a complex conditional 
syllogism, of which the major premise contains 
two or more conditional propositions, and the 
minor a disjunctive proposition; as, 

If A is B, is D, and if E is F, G is H; 
But either A is B or E is F; 
Therefore, C is D or G is H. 

If iEsckines joined in the public rejoicings he is incon- 
sistent ; if he did not he is unpatriotic ; 

But ^Eschines either did or did not join in the public 
rejoicings ; 

Therefore, he is either inconsistent or unpatriotic. 

The advantage of the Dilemma is this : that 
you may not be able to affirm or deny any 
proposition, but you may always state it dis- 
junctively. Demosthenes might not be able to 
prove that JEschines did join in the public re- 
joicing, or that he did not join ; but certainly 
he did or he did not. 

This Dilemma may easily be reduced to two 



DILEMMA. 81 

or more conditional syllogisms and these to 
regular syllogisms. 

36. Thus all hypothetical syllogisms as well 
as all other arguments may be reduced to regu- 
lar syllogisms, and so subjected to the test of 
the logical axiom. But it is more convenient 
in ordinary practice to try them by their own 
rules. 

EXAMPLES. 

1. If this man has a fever, he is sick ; 
But he is sick ; 

Therefore, he has a fever. 

2. The world was created by chance, or by 

an intelligent agent ; 
But it was not created by chance; 
Therefore, it was created by an intelli 

gent agent. • 

3. If Louis Philippe is a good king France is 

likely to prosper ; 
But Louis Philippe is a good king ; 
Therefore, France is likely to prosper. 

4. If C be not the center of the circle some 

other point must be ; 
But no other point can be the center ; 
Therefore, C is the center of the circle. 



82 ELEMENTS OF LOGIC. 

5. If this man were wise he would not speak 

irreverently of the Scriptures in jest; 

if he were good, he would not do so in 

earnest ; 
But he does it either in jest or in earnest ; 
Therefore, he is either not wise or he i& 

not good. 

6. If logic is useless it deserves to be neg- 

lected ; 

But logic is not useless ; 

Therefore, it does not deserve to be neg- 
lected. 

7. Either money or produce will be scarce 

in the market; 
But produce will not be scarce ; 
Therefore, money will be scarce. 

8. If W. were a general he would have 

power ; 
But W. is not a general ; 
Therefore, he has not power. 

9. If W. be a general he must be obeyed ; 
But ~W. must be obeyed ; 
Therefore, he is a general. 



DISTINCTIONS OF REASONING. 83 

SECTION Y. 

DISTINCTIONS OF REASONING. 

1. The divisions of reasoning into Deduction 
and Induction, Mathematical and Moral, De- 
monstrative and Probable, by Analogy, A 
priori, A posteriori, A fortiori, Reductio ad ab- 
snrdnm, and Reductio ad impossibile, are only 
different ways of laying down premises, the 
process of reasoning being always the same, 
namely, deductive — from generals to particulars. 

The degree of certainty in the conclusion, 
when the process of inference is correct, 
depends upon the degree of certainty in the 
premises. 

2. In Pure Mathematical Reasoning, the 
principles and judgments being always self-evi- 
dent, the conclusions are absolutely certain ; in 
Mixed Mathematics self-evident axioms and 
judgments are mixed with matters of fact 
and measurements of instruments, to which 
some uncertainty is attached; consequently 
the same uncertainty attaches to the conclu- 
sion. 



84 ELEMENTS OF LOGIC. 

EXAMPLE. 

If a straight line meet another straight line, 
the sum of the adjacent angles will be equal to 
two right angles. 

Suppose the straight line DC E 

meets the straight line A B 
at the point C; then will the 
angles A C D and D C B to- A G B 
gether be equal to the two right angles ACE 
and E C B. 



Axiom. — A whole is equal to the sum of all its parts. 
A D is a whole of which A E and E D are its 



Therefore, A D is equal to all its parts, namely, 
A E and E D. 

Axiom. — If equals be added to equals the sum is equal ; 
DOB added to A D, and D B added to A E 
plus EOD are equals added to equals. 
Therefore, the sum is equal. 

Now, as A C E is one of the right angles in 
question, you have only to prove that the other 
two angles E C D and D C B equal the other 
right angle E C B. 



DISTINCTIONS OF REASONING. 85 

The sum of all the parts is equal to the whole. 

EOD plus D B are all the parts of the angle EOB. 

Therefore, they are equal to the whole EOB. 

Thus you have proved that D C B added to 
A C D is equal to A C E added to E C B. 

This is a case of pure mathematics, because I 
have supposed ~D C a straight line meeting 
another A B ; but if I take a rod and make a 
line between two points on a field, I do not know 
that it is in reality a perfectly straight line. 
Hence, there is a mixture of practical uncer- 
tainty, with the absolute certainty of the 
axioms employed in any calculation about it ; 
hence, such calculation is called mixed mathe- 
matics. 

3. Induction is a course of argument by 
which, from the principles of causation, joined 
with particular phenomena, we infer the gen- 
eral law of those phenomena. 

Some of the principles of causality are the fol- 
lowing : JVo event, no phenomenon happens 
without a cause. Like material causes produce 
like effects. JVo cause can operate where it is 
not. 

From the principles we directly infer the pos- 
tulate : The immediate and invariable antecedent 



86 ELEMENTS OF LOGIC. 

of any 'phenomenon may be presumed to be its 
cause or contain its cause. 

In respect to spiritual agencies the principles 
of causation are the same, except in relation to 
the will, whose distinguishing characteristic is 
freedom. Of this alone we cannot predicate 
that like causes will produce like effects. We 
cannot certainly know how it will behave under 
any circumstances. 

It should be observed, that it may be beyond 
human power to perceive, when any physical 
change takes place, what the real cause is; 
but we know that it must be found where the 
event takes place, and that the invariable and 
immediate antecedent of the event must con- 
tain it. 

To discover the cause, therefore, of any phe- 
nomenon, we must observe under what circum- 
stances that phenomenon happens and notice its 
invariable antecedent. 

Having done this we are prepared to make 
the proper inference, and the whole process can 
be put into a syllogism with the particular 
cause, as discovered in one or two cases, for a 
minor premise, and a principle of causation for 
a major premise. The principles of causality 



DISTINCTIONS OF REASONING. 87 

are intuitively true, like the axioms of mathe- 
matics ; hence, induction has the same certainty 
as mixed mathematics. 

EXAMPLE. 

The law of magnetic attraction, or that the 
magnet will always attract iron, is proved thus : 

A material cause will always produce the same effect. 

Or, more particularly, 

Whatever is the cause of the attracting of iron in one 
or two cases will always attract iron ; 
A magnet is the cause of attracting iron in one or two 



Therefore, it will always attract iron. 

Now how do we know that it was the 
magnet and not something else that caused the 
iron to move ? 

We must make several experiments, and 
apply the following rule : 

RULE FOR OBSERVATION. 

If a phenomenon he preceded by anything, so 
that when that thing is present in different cir- 
cumstances that phenomenon takes place, but 



88 ELEMENTS OF LOGIC. 

does not take place when that thing is absent, 
though the circumstances remain the same, then 
that thing is the cause of the phenomenon or 
contains the cause. 

This rule will show, on making a few experi- 
ments, that the magnet is the cause of the at- 
traction of iron. 

Some things will not admit of the latter part 
of the rule being applied, as matter, gravita- 
tion, electricity, etc., can never be absent from 
any event in this world. 

This rule in its two parts may be symbolically 
exhibited thus: 

Part I.— A BO. A D E. 
a b c. a d e. 

Let a represent a phenomenon, and A some- 
thing supposed to be its cause. In one case A 
has the circumstances or adjuncts B C, in the 
other case different circumstances, D E. Now 
a appearing with A in different circumstances 
shows the latter to be its cause. 

Part II.— Now, if we have ABC. B C, 

a b c. be, 
this will show the absence of a when A is 
absent, though the circumstances which at- 
tended A remain the same. 



DISTINCTIONS OF KEASONING. 89 

Sometimes the particular cause is obtained by- 
testimony or revelation, and you have only to 
supply the major premise. Thus, we know God 
predicted contingent events in the prediction 
concerning the sins of Judas and Peter, and 
from this we prove his absolute foreknowledge. 

In this case the arguments would stand thus : 

Whoever can predict contingent events foreknows all 
things. 

God has predicted contingent events ; 
Therefore, God foreknows all things. 

To prove the minor premise we may say — 

Human transgressions are contingent events ; 
God has predicted human transgressions in the case of 
Judas and Peter ; 

Therefore, God has predicted contingent events. 

By induction the psychologist discovers dis- 
tinctions between the powers of the mind ; for 
example, that sensation and perception cannot 
give the idea of space, but some other power 
called intuition or the reason. 

4. Reasoning from Analogy is arguing with 
premises made up of principles and judgments 
respecting similar things, or things that are alike 
in some relations. This definition would in- 
clude induction, as treated by most writers on 



€0 ELEMENTS OP LOGIC. 

the subject; but I consider the difference to 
be very important, because the principles on 
which Induction is based are certainties, but 
those of Analogy are but probabilities. 

Some of the principles on which reasoning by 
Analogy is based are : 

Similar causes will be likely to produce simi- 
lar effects. 

Things that resemble each other in certain at- 
tributes or relations will be likely also to resem- 
ble each other in some other attributes or relations. 

An attribute found in several individuals be- 
longs to their class. [This is the old principle of 
induction.] 

Thus, horned animals have cloven hoofs, is a 
law in natural history, and is proved thus : 

Animals that resemble each other in some attributes are 
likely to resemble each other in other attributes ; 

All horned animals resemble the ox, sheep, etc., in being 
horned ; 

Therefore, they will be likely to resemble them in other 
attributes as having cloven hoofs. 

In the following example the conclusion dis- 
agrees with facts : 

An attribute of a, b, and c clovers is likely to belong to 
the whole class; 

Having three leaves is an attribute of a, b, and c clovers , 
Therefore, it is likely to belong to the whole class. 



DISTINCTIONS OF. REASONING. . 91 

5. Seasoning a Priori is reasoning from 
antecedents to consequents. Thus, the idea 
of God, the perfect and infinite One, is proved 
true by the pre-existing ideas of infinity and 
perfection. 

Every necessary and universal idea of the human mind 
must indicate a reality ; 

The ideas of the perfect and infinite are necessary and 
universal in the human mind ; 

Therefore, they indicate a reality. 

6. Reasoning a Posteriori is reasoning from 
consequents to antecedents. 

Whatever exhibits marks of design proves an intelligent 
author ; 

The world exhibits marks of design ; 

Therefore, the world proves an intelligent author. 

T. Reasoning a Fortiori is inferring a judg- 
ment from premises which have already been 
admitted to prove a point less probable. 

If robbery deserves imprisonment, much more does 
highway robbery. 

If God foresees contingent events he must foresee neces- 
sary events. 



92 ELEMENTS OF LOGIC. 

8. Eeductio ad absurdum is proving that a 
certain proposition is true, because its contra- 
diction involves an absurdity. 

9. Eeductio ad ihpossebile is proving a pro- 
position to be true by showing that its contra- 
diction is inadmissible. 

These are often employed in mathematics. 

10. Probable reasoning is drawing infer- 
ences from premises that are not certain, but 
more or less probable. 

When both premises are of this character 
then the result is not so probable as either pre- 
mise, but as a fraction of one of them. 

Thus, if the probability of the arrival of ocean 
mail to-day may be represented by f, and the 
probability of your receiving letters by it is £, 
then the probability of your receiving letters 
to-day is but \ of f, that is, \. 

The rule is to represent the probability of 
each premise as compared with certainty by a 
fraction, and multiply these fractions together 
for a result. 

EXAMPLES. 

1. Thirty-two degrees Farenheit will always 
freeze water. 



DISTINCTIONS OF REASONING. 93 

2. Swans are white. 

3. Jupiter is inhabited. 

4. If one straight line cross another straight 

line the opposite angles are equal. 

5. The freedom of the will is proved by the 

idea of liberty. 

6. The shadow of the earth upon the .moon 

proves that it is round. 

7. If highway robbery and murder deserve 

death, piracy deserves death. 

8. A certain reporter is generally correct, 

say five times out of six. A certain 
statement is probably his report, the 
probability being represented by two 
fifths, what is the probability of the 
report being true ? 

9. If the probability of your winning a game 

be one half, what is the probability 
of your winning three games in suc- 
cession ? 

10. The law of terrestrial gravitation is proved 

by an apple falling to the ground. 

11. A certain degree of attention is necessary 

to memory, as experience demonstrates. 

12. Swine have horns, if what is true of 

individuals is true of a class. 



94 ELEMENTS OF LOGIC. 

13. This servant will always return in due 

season, because he always has done so. 

14. The emperor will declare war, because 

he never submits to a national insult. 

15. The will is free, and therefore its future 

acts are unknown by even an infinite 
mind. 

16. Retribution may be expected in a future 

state, judging from the effects of virtue 
and vice in this life. 

17. The will never acts without some motive, 

and therefore, if you know a man's 
motives in any case, you may know 
how he will choose. 

18. This case is typhus fever, for it exhibits 

many symptoms of that disease. 

19. Mercury, Venus, and the Earth are 

opaque, and therefore all the planets 
are opaque. 

20. The bull-dog, terrier, mastiff, etc., bark ; 

therefore, all dogs bark. 

21. Quadrupeds, birds, fishes, etc., have a 

^ nervous system; therefore, all animals 
have a nervous system. 



PART IV. 



OF FALLACIES. 

1. The fourth part of Logic treats of Falla- 
cies. 

2. A Fallacy is an unsound argument of 
any kind. 

3. Fallacies are of two kinds ; logical falla- 
cies and material fallacies. 

4. I. Logical Fallacies are those which in 
form violate any of the rules of syllogism. 

In these the error is entirely in the process 
of reasoning, and the conclusion does not follow 
from the premises ; as, 

Every rational agent is accountable ; 
Brutes are not rational agents ; 
Therefore, brutes are not accountable. 

This violates the third rule of syllogism. 

5. II. Material Fallacies are those which 
in form do not violate any of the rules of syl« 



96 



ELEMENTS OF LOGIC. 



logism, but the premises either are not wholly 
true in fact, are unduly assumed, or result in a 
conclusion not relevant to the question which is 
argued. 

In material fallacies the fault is entirely in 
the matter of the propositions, and not in their 
form or connection. 

All bodies move toward the center of the universe ; 
All bodies move toward the center of the earth ; 
Therefore, the center of the earth is the center of the 
universe. 

In this example there is no fault in the pro- 
cess of reasoning; the conclusion results from 
the premises, but the minor premise contains a 
statement which is not true in fact. 

f^lp^ Some logicians make a third division. of 
fallacies into semi-logical, including those made 
by ambiguous terms: for if these terms are used 
in two senses they make a logical fallacy; and if 
they are used in only one sense they make a 
material fallacy ; and you cannot always tell 
which. A simple instance is the following: 

Light is contrary to darkness ; 

Feathers are light; 

Therefore, feathers are contrary to darkness. 



OF FALLACIES. 97 

0. Fallacies are rarely presented in the syl- 
logistic form. They are usually found in enthy- 
memes, and the error lurks in the suppressed 
proposition. 

Sometimes they are offered in the form of 
questions so stated that a false conclusion will 
be likely to be implied. 

7. Whately remarks, All jests are fallacies. 
They tend to excite laughter by betraying their 
fallacious character while putting on the air of 
serious argument. The contrast amuses. For 
example: A gentleman seeing a young man 
whom he knew going by with a looking-glass, 
cried out, "Ah, Joseph, don't carry that glass 
about, it will reflect on you." This, reduced to 
a syllogism, will be found to violate the first rule 
of syllogism, by having an equivocal middle. 

8. To determine whether an argument be 
valid or fallacious, let the following directions 
be followed. 

EULE. 

Reduce the argument to a syllogistic form. 
If it he found incapable of taking that form 
it is of course a fallacy. If it he reducihle to a 
syllogism, ohserve carefully the import and the 
number of its terms and propositions, and apply 



98 ELEMENTS OF LOGIC. 

the rules of syllogisms. If it violates any of 
them it is a logical fallacy. If not, observe if 
either of the premises be untrue or inadmissible, 
or the same as the conclusion, or result in a con- 
clusion different from the one required. If so 
it is a material fallacy. 

SECTION I. 

LOGICAL FALLACIES. 

9. It is evident that logical fallacies are as 
numerous as are the ways of violating the five 
rules of syllogism. 

Most of those made by ambiguous terms may 
be classified as follows : 

10. I. The Fallacy of Equivocation, arising 
from an equivocal word, or from the ambiguous 
structure of the sentence. 

This class will be found to violate the first 
rule of syllogism ; as, 

All that believe shall be saved ; 

The devils believe ; 

Therefore, the devils shall be saved. 

Every one desires happiness; 

Virtue is happiness ; 

Therefore, every one desires virtue. 



LOGICAL FALLACIES. 99 

In the first example the term believe is equiv- 
ocal, having two different senses. There is, 
therefore, in reality, two terms ; and the syllo- 
gism, consequently, has four terms, which is con- 
trary to Rule I of syllogisms. In the second 
example the minor premise is ambiguous. 

11. II. The Fallacy of Similar Expression 
arises from words that are derived from the 
same root and are similar in sound, but not in 
sense ; such as art, artful; faith, faithful; 
design, designing. As, 

Designing men should be avoided : 
This man has many designs ; 
Therefore, he should be avoided. 

This violates Rule I of syllogism, for there are 
in reality four terms. 

12. III. The Fallacy of Composition or Di- 
vision is when the middle term is used collect- 
ively in one premise, and not collectively, but 
distributively, in the other. As, 

Two and three are even and odd ; 
Five is two and three ; 
Therefore, five is even and odd. 

This is a fallacy of composition. Two and 
three is the middle term, and it is used distrib- 



100 ELEMENTS OF LOGIC. 

ntively in the major premise, and collectively 
in the minor premise. Hence there are properly 
four terms in this argument, which is contrary 
to Rule I of syllogism. 

The planets are seven ; 
Mercury and Venus are planets ; 
Therefore, Mercury and Yenus are seven. 

This is a fallacy of division. The middle 
term is used distributively in the minor premise, 
and collectively in the major. 

13. IV. The Fallacy of Accident is when 
the middle term is understood simply and as to 
its essence, in one premise, but in the other is so 
used as to imply that something, which does 
not belong to it essentially, but accidentally, is 
taken into account with it. As, 

Whatever is bought in the shambles is eaten by man ; 
Eaw meat is bought in the shambles ; 
Therefore, raw meat is eaten by man. 

Here the middle term is 'bought in the 
shambles, and it is used in the minor premise, 
as considered simply, and as to its essence ; but 
in the major premise it should be understood in 
connexion with something else, as, when prop- 



LOGICAL FALLACIES. 101 

erly cooked. Hence, four terms are employed 
in reality in this argument which violates Rule I 
of syllogism. 

EXAMPLES. 

1. ISTo one is rich who has not enough ; 
No miser has enough ; 
Therefore, no miser is rich. 

2. All that glitters is not gold ; 
Tinsel glitters ; 
Therefore, tinsel is not gold. 

3. He who calls you a man speaks truly ; 
He who calls you a fool calls you a man ; 
Therefore, he who calls you a fool speaks 

truly. 

4. Warm countries alone produce wine ; 
Spain is a warm country ; 
Therefore, Spain produces wine. 

5. What we eat grew in the fields ; 
Loaves of bread are what we eat ; 
Therefore, loaves of bread grew in the 

fields. 

6. What is universally believed is true ; 
The existence of a God is true ; 
Therefore, the existence of a God is uni- 
versally believed. 



102 ELEMENTS OF LOGIC. 

7. Whatever is universally believed must 

be true ; 

The immortality of the soul is not uni- 
versally believed ; 

Therefore, it is not true. 

8. What I am you are not ; 
But I am a man ; 
Therefore, you are not. 



SECTION II. 

MATERIAL FALLACIES. 

14. Material fallacies may be as numerous as 
errors of learning, mistakes of judgment, or 
willful duplicity can make them. 

The most common may be included in the 
following classes: 

15. I. The Fallacy of begging the ques- 
tion is that of inferring a conclusion from pre- 
mises substantially the same as the conclusion, 
or depending upon the conclusion ; as when we 
attempt to prove a thing by itself, or by a 
synonymous word, or by something which is 
itself to be proved by the very point you seek 
to establish. As, 



MATERIAL FALLACIES. 103 

God is eternal, because he is without beginning or end. 

Opium produces sleep because it is soporific. 

We know the Scriptures are true from the infallible 
testimony of the Church, and we know the Church is in- 
fallible by the declaration of the Scriptures. 

The last example is what is called reasoning 
in a circle. 

16. II. The Fallacy of false assumption is 
when the premises are unduly or unwarrant- 
ably assumed ; as when we attempt to prove a 
thing by something that is false, or unknown, or 
partially stated. As, 

All bodies that move themselves are animated ; 
All stars and heavenly bodies move themselves ; 
Therefore, the stars and all the heavenly bodies are 
animated. 

Meteors have a volcanic origin ; 

1% they cannot otherwise be accounted for. 

We hold this doctrine to be true by the authority of 
St. Paul in such and such texts. 

This is a fallacy, if these texts do not contain 
the whole of the apostle's testimony to the point 
in question, and is sometimes called the fallacy 
of partial reference. 

17. III. The Fallacy of mistaking the ques- 
tion is that in which the premises are such as 



104 ELEMENTS OF LOGIC. 

result in a conclusion different from the one 
required, but apparently the same. As, 

Alfred the Great was a scholar ; 

For he founded the University of Oxford. 

18. The sophist will not always draw out the 
conclusion, but leave it to be inferred, for in 
that case its irrelevancy will be less likely to be 
detected. 

19. This fallacy is often conveyed in appeals 
to prejudice, to the passions, or to personal 
considerations; sometimes in the form of ob- 
jections, and sometimes by implication, in ar- 
guments, which go to prove a part of what is 
required. As, 

Gentlemen of the jury, this man is a friend to the rights 
of the people. "Will you convict him ? 

This work is not evangelical. Look at the statements 
made in the eighth chapter. Are these warranted by the 
New Testament ? 

These objections are many and weighty. Can such a 
science be worthy of credit ? 

EXAMPLES. 

1. The soul occupies the whole body, for it 
resides in every member. 



MATERIAL FALLACIES. 105 

2. The plant is capable of much growth, for 

it has great vegetative powers. 

3. The soul suffers dissolution with the body 

at death. See Ecc. iii, 18, 19, 20 ; Job 
xxxiv, 15 ; Psa. cxlvi, 3, 4. 

4. The Bible cannot be the rule of faith, for 

men understand it very differently. 

5. We may expect some dreadful disaster, for 

the sky last night was full of falling 
meteors. 

6. The appearance of strange birds flying 

south in the highest northern latitudes 
which have been explored, and of float- 
ing plants, as well as men who declare 
by signs that they come from the far 
north, indicate that the earth is concave 
about the poles, and the interior of the 
earth is inhabited. 

7. Mohammed is a prophet, for the Koran de- 

clares it ; and the Koran is true, for Mo- 
hammed received it from God, as he 
affirms. 

8. Whatever is contrary to experience is not 

to be believed. 
Miracles are contrary to experience ; 
Therefore, miracles are not to be believed. 



106 ELEMENTS OF LOGIC. 

9. Paul was not a Roman citizen, for he was 

born at Tarsus in Cilicia. 

10. Job was a great sinner, for he was over- 

whelmed with great calamities. 

11. "No evil should be allowed that good may 

come of it ; 

All punishment is an evil ; 

Therefore, no punishment should be al- 
lowed that good may come of it. 

12. No man can possess power to perform an 

impossibility ; 
A miracle is an impossibility; 
Therefore, no man can possess power to 

perform a miracle. 

13. Which of you having an ox or an ass fall 

into a pit, will not pull him out on the 
Sabbath day? 
The last is a personal appeal, called Ar- 
gumentum ad hominem, and is allow- 
able when your object is to silence the 
captious. As offered to prove the 
point in question, it is a fallacy. (19.) 



SUPPLEMENT. 



SECTION I. 

MOODS AND FIGURES OF SYLLOGISMS. 

This subject may be advantageously studied 
after the scholar has become perfectly familiar 
with the foregoing, and is expert in the applica- 
tion of all the rules of logic. In that case it 
may serve to discipline the mind, otherwise it 
will only perplex. One may be an able logician 
without the doctrine of moods and figures. 

1. The Mood of a Syllogism is the designa- 
tion of the quantity and quality of its proposi- 
tions. 

This is done by the symbols A, E, I, and O, 
which stand respectively for the universal af- 
firmative, universal negative, particular affirma- 
tive, and particular negative. 



108 ELEMENTS OF LOGIC. 

The following, for example, is A, A, A. 

A. All animals are mortal ; 

A. All men are animals ; 

A. Therefore, all men are mortal. 

The following is E, A, E. 

E. No human invention is perfect ; 
A. Language is a human invention ; 
E. Therefore, no language is perfect. 

2. The whole number of the moods of valid 
syllogisms is only eleven. A, A, A, — A, A, I, — 
A, E, E,— A, E, O,— A, I, I,— A, O, O— E, A, 
E,— E, A, O,— E, I, 0,-1, A, 1,-0, A, O. 

3. As there are sixty-four different ways in 
which it is possible for A, E, I, O to be com- 
bined to form a syllogism, there might be fifty- 
three other moods formed, as E, E, A, — I, I, I, 
etc. ; but they would offend against one or more 
of the five rules of syllogism. As, 

I. Some birds are animals ; 

I. Some fish are animals ; 

I. Therefore, some fish are birds. 

E. No human invention is perfect ; 

E. No language is perfect ; 

A. Therefore, language is a human invention. 



MOODS AND FIGURES OF SYLLOGISMS. 109 

These examples are contrary to the fifth rule 
of syllogisms. Two negative or two particular 
premises prove nothing. 

4. The Figure of a Syllogism denotes the 
situation of the middle term, in respect to the 
major and minor terms. 

5. Figure First is when the middle term is 
'the subject of the major premise and the pre- 
dicate of the minor premise. As, 

A. Every wicked man is miserable ; 

A. Every tyrant is a wicked man ; 

A. Therefore, every tyrant is miserable. 

E. No discontented man is a happy man ; 
A. Every wicked man is a discontented man ; 
E. Therefore, no wicked man is a happy man. 

A. All the faithful are dear to God ; 
I. Some that are afflicted are faithful ; 
I. Therefore, some that are afflicted are dear to God. 

E. - No virtue is an evil ; 
I. Some difficult things are virtues ; 
O. Therefore, some difficult things are not evils. 

6. To this figure the logical axiom applies 
directly ; and to this figure all the other figures 
may be reduced. 



110 ELEMENTS OF LOGIC. 

7. Figure Second is when the middle term is 
the predicate of both the major and the minor 
premises; as, 

E. No happy man is discontented ; 

A. Every wicked man is discontented ; 

E. Therefore, no wicked man is a happy man. 

A. Every wicked man is discontented ; 

E. No happy man is discontented ; 

E. Therefore, no happy man is a wicked man. 

E. No evil is a virtue; 
I. Some difficult things are virtues ; 
0. Therefore, some difficult things are not evils. 

A. Every good man is afflicted ; 
O. Some rich men are not afflicted ; 

0. Therefore, some rich men are not good men. 

8. Figure Third is when the middle term is 
the subject of both the premises. As, 

A. All the faithful are dear to God ; 
A. All the faithful are afflicted ; 

1. Therefore, some that are afflicted are dear to God. 

I. Some of the faithful are afflicted ; 
A. All the faithful are dear to God ; 
I. Therefore, some that are dear to God are afflicted. 



MOODS AND FIGURES OF SYLLOGISMS. Ill 

A. All the faithful are dear to God ; 
I. Some of the faithful are afflicted; 
I. Therefore, some that are afflicted are dear to God. 

E. No virtue is an evil ; 
] A. All virtues are difficult ; 
O. Some difficult things are not evils. 

O. Some called Christians are not true believers ; 
A. All called Christians profess faith ; 

0. Therefore, some who profess faith are not true 
believers. 

E. No virtue is an evil ; 

1. Some virtues are difficult. 

O. Therefore, some difficult things are not evils. 

9. Figure Fourth is when the middle term is 
the predicate of the major and the subject of 
the minor premise. 

10. This is the reverse of the first figure and 
is the most awkward of all. As, 

A. Every tyrant is a wicked man ; 
A. Every wicked man is miserable ; 
I. Therefore, some that are miserable are tyrants. 

A. Every wicked man is discontented ; 

E. No discontented man is happy ; 

E. Therefore, no happy man is a wicked man. 



112 ELEMENTS OF LOGIC. 

I. Some afflicted are faithful ; 
A. All the faithful are dear to God ; 
I. Therefore, some that are dear to God are afflicted. 

E. No evil is a virtue ; 

A. All virtues are difficult ; 

O. Therefore, some difficult things are not evils. 

E. No evil is a virtue ; 
I. Some virtues are difficult ; 
0. Therefore, some difficult things are not evils. 

11. Each of the eleven allowable moods will 
not go in every figure, for it will violate some 
of the rules of syllogism in one figure, though 
not in another. For example, A, A, A, which 
goes in the first figure will not go in the third 
figure. 

Figure 1st. All wicked men are miserable; 
All tyrants are wicked men ; 
Therefore, all tyrants are miserable. 

Figure 3d. All wicked men are miserable ; 
All wicked men are tyrants ; 
Therefore, all tyrants are miserable. 

This violates Eule III of syllogism, for the 
term tyrants is distributed in the conclusion, 
though not in the premises. Besides, the minor 
premise is incorrect. 



MOODS AND FIGURES OF SYLLOGISMS. 113 

12. Some of the moods, also, which might be 
j admitted in some of the figures are useless, as 
i having a particular conclusion when the uni- 
i versal might be drawn. 

For example, A, A, I will go in the fourth 
. figure, but in the first figure it is useless. 

Figure 4th. A. Every tyrant is a wicked man ; 

A. Every wicked man is miserable ; 

I. Therefore, some that are miserable are 
tyrants. 

Figure 1st. A. Every wicked man is miserable ; 

A. Every tyrant is a wicked man ; 

A. Therefore, every tyrant is miserable. 

But, 

I. Therefore, some tyrants are miserable: 

would be a useless conclusion, for a universal 
conclusion is legitimate. 

13. For these reasons, out of the forty-four 
allowable moods, which mighty possibly go into 
the four figures, only nineteen are retained. 
Examples of all the nineteen are found above 
under the definitions of the four figures. 

14. To assist in remembering these moods, 
and the figure in which they are found, the fol- 
lowing mnemonic lines have been invented : 



114 ELEMENTS OF LOGIC. 

First. bArbA'rA, cElA'rEnt, dArl'I, fErl'O. 
Second. cEsA'rE, cAmE'strEs, f Estl'nO, bArO'kO. 
Third. dArA'ptl, dlsA'mls, dAtl'sI, fElA'ptOn, 

bOkA'rdO, f Erl'sO. 
Fourth. brAmA'ntlp, cAmE'nEs, dlmA'rls, fEsA'pO, 
frEsI'sOn. 

Here, it will be seen, are only ten moods ; 
but some are employed in more than one figure, 
as E, I, O, making nineteen in all the four 
figures. 

15. If any syllogism be not found in these 
lines it cannot be a valid syllogism ; it is a 
logical fallacy. 

16. The utility of the mnemonic lines is like 
that of duly certified weights and measures, by 
which we test the size or weight of bodies with- 
out the necessity of a minute and tedious calcu- 
lation. 

SECTION II. 

REDUCTION. 

17. The process by which the moods of the 
last three figures are changed into a mood of 
the first figure is called Reduction. 

18. This is done in two ways; by Ostensive 
Reduction and by Reductio ad impossible. 



KEDUCTION. 115 

19. Ostensive Eeduction is performed by 
the conversion of one of the premises, A into 
I, E into E, I into I, and by transposing the 
premises when occasion requires. 

For example, take Cesare of the second 
figure. 

cEs. No happy man is discontented ; 
A. Every wicked man is discontented; 
rE. Therefore, no wicked man is a happy man. 

This may be converted into Celarent of the 
first figure by the simple conversion of the 
major term, thus : 

cE. No discontented man is a happy man ; 
1A. Every wicked man is a discontented man; 
rEnt. Therefore, no wicked man is a happy man. 

Take now Camestres of the second figure and 
convert that also into Celarent. To do this you 
will only have to convert the minor premise 
and transpose the premises, as will be seen in 
the following examples. 

cAm. Every wicked man is discontented ; 
Es. No happy man is discontented; (convert and 
transpose.) 
trEs. Therefore, no happy man is a wicked man. 



116 ELEMENTS OF LOGIC. 

cE. No discontented man is a happy man ; 
1A. Every wicked man is discontented ; 
rEnt. Therefore, no wicked man is a happy man. 

20. In like manner all the moods of the last 
three figures can be reduced into one of the four 
perfect moods of the first figure. 

21. In the mnemonic lines the initial letters 
5, <?, <#, y, show to which mood of the first figure 
the reduction is made, namely, harhara, celarent, 
darii, or ferio. The letter m signifies that the 
premises are to be transposed, as above, in 
Camestres; the letter s denotes that the propo- 
sition, which the preceding vowel stands for, is 
to be converted by simple conversion, and j?, 
by particular conversion ; but p in Bramantip 
marks that the premises, when changed, warrant 
a universal conclusion instead of a particular. 
The symbols A E I O mark the moods, that is, 
the quality or quantity of the propositions. 

22. Reductio ad Impossibile is when you 
reduce a mood to the first figure, by substitut- 
ing the contradictory of the conclusion for one 
of the premises ; by which an absurdity follows 
which proves not directly that the conclusion is 
true, but that it cannot be false. 

Thus Baroko* in the second figure, 



REDUCTION. 117 

bAr. Every good man is afflicted ; 
Ok. Some rich men are not afflicted ; 
O. Therefore, some rich men are not good men. 

bAr. Every good man is afflicted ; 
bA. All rich men are good men ; 
rA. Therefore, all rich men are afflicted. 

Which conclusion is notoriously false, and the 
original conclusion which you had drawn is, 
therefore, true. 

23. The letter, h in the mnemonic lines de- 
notes that the proposition indicated by the 
vowel immediately preceding is to be substi- 
tuted by the contradictory of the conclusion ; 
the other letters, not above explained, have no 
signification. 

EXAMPLES. 

1. Whoever has reflection and volition has 

the essential properties of mind ; 

Mankind has reflection and volition ; 

Therefore, mankind has the essential prop- 
erties of mind. 

2. Whatever is universally believed must be 

true; 
The existence of God is not universally 

believed ; 
Therefore, it is not true. 



118 ELEMENTS OF LOGIC. 

3. Whoever is capable of deliberate crime is 

responsible ; 
An infant is not capable of deliberate 

crime ; 
Therefore, an infant is not responsible. 

4. Some philosophers reckon virtue good in 

itself ; 

The Epicureans did not reckon virtue good 
in itself; 

Therefore, the Epicureans were not phil- 
osophers. 

5. Prudence has for its object the benefit of 

individuals ; 
But prudence is a virtue ; 
Therefore, some virtue has for its object 

the benefit of individuals. 

6. Whatever is expedient is conformable to 

nature. 
Whatever is conformable to nature is not 

hurtful to society. 
Therefore, what is hurtful to society is 

never expedient. 

7. No man is happy who is not secure ; 
No tyrant is secure; 
Therefore, no tyrant is happy. 



EXAMPLES. 119 

8. All true patriots are friends to religion ; 
Some great statesmen are not friends to 

religion ; 
Therefore, some great statesmen are not 
true patriots. 

9. All true Christians have peace ; 

Some afflicted men are true Christians ; 
Therefore, some afflicted men have peace. 

10. No uncandid man is fit to reason correctly; 
Some infidels are uncandid ; 
Therefore, some infidels are not fit to 

reason correctly. 

11. E, E, E,—I, O, 0,-1, E, O. 

12. I, A, I,— A, E, E, in the first figure. 

13. A, A, A in the third figure, A, E, O. 



120 ELEMENTS OF LOGIC. 



QUESTIONS IN A GENERAL REVIEW. 

1. What is Logic? 

2. What does it assume as its foundation ? 

3. What are first truths ? 

4. What are first principles ? 

5. What is the true process of reasoning ? 

6. What is Aristotle's dictum ? 

7. What is a distributed term ? 

8. What are the rules of distribution ? 

9. What is opposition? 

10. What is conversion ? 

11. What two canons have logicians inverted 

to test the validity of arguments ? 

12. What five rules must be observed ? 

13. What are hypothetical syllogisms? 

14. What two kinds of these ? 

15. Can they be reduced to one ? 

16. Can they be reduced to categoricals ? 

17. What is a dilemma. 

18. What is the special advantage of it ? 

19. What distinctions of reasoning a 

found ? 

20. Are these different in principle ? 

21. What division of fallacies is made ? 



APPENDIX. 



I. 

THE PHILOSOPHY OF INDUCTION.* 

It has long been the fashion to decry the 
logic of Aristotle, because, its legitimate use 
not being understood in the medieval schools, 
it served to divert the minds of men from the 
study of nature, and set them whirling about in 
dialectic circles to educe the principles of science 
and the laws of the universe ; and Bacon and 
Des Cartes have been lauded to the skies, be- 
cause they taught that nature reveals her laws 
only in the passing phenomena of matter and 
mind, as presented to the senses and the con- 
sciousness, which must be carefully analyzed 

* First delivered before tfie Philosophical Society of Dickinson 
College. 1853. 



122 ELEMENTS OF LOGIC. 

and then generalized by the process of induction. 
A comparison has been made between the or- 
ganon of Aristotle and the organon of Bacon, 
or, to speak more precisely, between the method 
of deduction and of induction, altogether to the 
disparagement of the former, until at length it 
has come to pass that it is no longer regarded 
by many as of vital importance to scientific in- 
vestigation, while induction is considered as not 
merely an indispensable auxiliary to the dis- 
covery of new truths and principles, but as the 
only fundamental process of inference — the 
only process by which, from facts perceived by 
the intelligence, you can advance to the determ- 
ination of the laws and principles which are 
the objects of science. 

It is remarkable that, notwithstanding the 
exaltation of induction, since Bacon directed 
the attention of philosophers to it, no thorough 
attempts were made to expound its philosophy 
and to institute its canons until very recently. 
Dr. Whewell, Mr. John Stuart Mill, Dr. Henry 
Tappan, and Sir William Hamilton, and writers 
in other tongues, have supplied the desideratum 
by works profoundly investigating the whole 
subject of logic, and particularly induction. 



THE PHILOSOPHY OF INDUCTION. 123 

"We have, therefore, the means by which we 
may sit in judgment upon the question and 
render an enlightened verdict. 

COUSIN'S VIEW OF INDUCTION. 

The particular aspect of the question which 
it is the design of this paper to examine, is 
clearly presented in the following remarks in 
Cousin's critique of the philosophy of Locke. 
Cousin wonders, as well he may, that a leader 
in the sensual and Baconian school of philoso- 
phy should so far be warped from his appropri- 
ate sphere of thought as to lose sight altogether 
of induction as one of the legitimate modes of 
knowledge, while, at the same time, casting 
contempt upon the syllogism as the proper type 
of the reasoning process ! 

"Thus intuition and demonstration are the 
different modes of knowledge, according to 
Locke. But are there no others? Have we 
not knowledge which we acquire neither by 
intuition nor demonstration? How do we ac- 
quire a knowledge of the laws of external 
nature ? Take which you please, gravitation for 
instance. Certainly there is no simple intuition 
and immediate evidence here, for experiments 



124 ELEMENTS OF LOGIC. 

multiplied and combined are necessary to give 
the slightest law ; and even this will not suffice, 
since the slightest surpasses the number, what- 
ever it be, of experiments from which it is 
drawn. There is need, therefore, of an inter- 
vention of some other operation of mind besides 
intuition. Is it demonstration? Impossible, for 
demonstration is the perception of the relation 
between two ideas by means of a third ; but it 
is upon the condition that the latter should be 
more general than the two others, in order to 
embrace and connect them. To demonstrate 
is, in the last analysis, to deduce the particular 
from the general. Now, what is the more gen- 
eral physical law from which gravitation can be 
deduced ? We have not deduced the knowledge 
of gravitation from any other knowledge an- 
terior to it, and which involves it in the germ. 
How, then, have we acquired this knowledge, 
which we certainly have ? and, in general, how 
do we acquire the knowledge of physical laws? 
A phenomenon having been presented a num- 
ber of times, with a particular character and in 
particular circumstances, we have judged that 
if this same phenomenon should occur in similar 
circumstances, it would have the same character; 



THE PHILOSOPHY OF INDUCTION. 125 

that is to say, we have generalized the particular 
character of this phenomenon. Instead of de- 
scending from the general to the particular, we 
have ascended from the particular to the gen- 
eral. This general character is w^hat we call a 
law : this law we have not deduced from a more 
general law or character; we have derived it 
from particular experiments in order to transfer 
it beyond them. It is not simple resumption 
nor a logical deduction ; it is what we call in- 
duction. It is to induction that we owe all 
conquests over nature, all our discoveries of the 
laws of the world." 

PROBLEM TO BE SOLVED. 

This clear and eloquent exposition of the 
order of thought in the two processes of deduc- 
tion and induction, as it has commonly been 
apprehended, enables us to present, without 
danger of being misunderstood, the problem 
which we wish to solve, namely, that there is 
no fundamental difference between induction 
and deduction ; but in both cases the mind pro- 
ceeds from the more general to the less general, 
or from the general to the particular; and that 
the opposite process of proceeding from the 



126 ELEMENTS OF LOGIC. 

particular to the general is utterly impossible. 
All inference, I maintain, is of one kind — it is 
deductive. You may take as many particulars 
as you can gather together, and they will be 
perfectly barren of any consequence, unless you 
can attach them to a general principle. You 
may sum them up and call it generalization, 
but you can never infer a universal law, you 
can make no scientific generalization by means 
of them, unless you can put them upon some 
broader general principle than that which you 
wish to educe from them. Take the instance 
of scientific induction referred to by Cousin, 
that of the law of gravitation, and analyze it 
thoroughly, and you will see that it is at bottom 
deduction. A philosopher observes a material 
substance — a body — say, an apple, fall to the 
ground ; he observes another body, a leaf, in 
like manner disengaging itself from the tree 
and following the apple ; he casts a stone into 
the air, it takes the same direction ; he casts a 
feather upon the winds, and, though for a time 
it is resisted by the currents of air, yet, when 
these obstacles cease, it directly in like manner 
falls to the earth. From these particulars he 
observes that it is the material substance in 



THE PHILOSOPHY OF INDUCTION. 127 

these different bodies that exhibits the phe- 
nomenon of falling to the earth, and not any 
particular quality of the apple, or the leaf, or 
the stone, or the feather; and this is his anatysis. 
Thereupon he proceeds to infer that all bodies — 
all material substances — in all parts of the globe 
will behave in like manner ; in other words, he 
infers the law of terrestrial gravity. This is his 
induction. He seems, indeed, merely to pro- 
ceed from the particular to the general ; but 
how? by what authority? on what ground? To 
answer this question is to solve the problem of 
induction. 

DR. WHEWELL'S SOLUTION. 

Dr. Whewell, who has elaborated this point, 
says that the conclusion is not a mere summing 
up of these particulars, and of all known par- 
ticulars of the same nature ; it is something 
more, a conception which, while it expresses 
these particulars, transcends them; it reaches 
all possible cases of the same kind. But how 
do we get this conception ? He says we leap to 
it: "Induction mounts the ladder by a leap, 
which is out of the reach of method." But 
then it can turn round and verify itself by de- 



128 ELEMENTS OF LOGIC. 

scending the ladder, step by step, by the de- 
ductive process. But how do we make the 
leap? By a sort of philosophical "sagacity — 
a scientific instinct — " which is the rare gift 
of some superior minds. But this explains 
nothing. 

ANALYSIS OP INDUCTION, BY J. S. MILL. 

Now, if this inference of the general law 
from observed particulars be a legitimate pror 
cedure, and it cannot admit of any solution, 
then it must be regarded as ultimate, and we 
may call it induction, and mark it as the 'oppo- 
site of deduction. But it happens that we can 
analyze the process in this instance and in all 
instances of induction; and this analysis will 
show that the subtle movement of the reasoning 
faculty from the particulars to the general is 
upon the broad basis of a universal and intuitive 
principle; and thus the whole process could 
easily be put into the form of a syllogism, 
with the principle for its major premise, 
and these observed particulars for its minor 
premise. 

Happily the desired analysis of this process is 
furnished to our hand by Mr. Mill, who not only 



THE PHILOSOPHY OF INDUCTION. 129 

goes with Cousin in maintaining that induction 
is one fundamental mode of investigation, but 
advances far beyond him, contending with great 
ability that inference is always fundamentally 
from particulars to generals, and that deduction 
is only an intermediary process, which may be 
resorted to for convenience, but is of no avail 
for original discovery. 

And here I can scarcely refrain from remark- 
ing how happily opposite systems conspire to 
advance the light of truth! By their conflict 
they bring to view the vital points of inquiry, 
and clear the ground for those who would ap- 
proach to determine the merits of the case. If 
Mr. Mill has taken the wrong side of this ques- 
tion, yet it will ever be to his praise that his 
thorough comprehension of the subject and his 
precise and candid statements have placed the 
controversy in the clearest light; and if logicians 
differ it will not be because the point in dis- 
pute is misapprehended, but because their dif- 
ferent systems of philosophy drive them to op- 
posite conclusions. Hear what he says : " We 
must first observe that there is a principle im- 
plied in the very statement of what induction 

is, an assumption with regard to the course of 
9 



130 ELEMENTS OF LOGIC. 

nature and the order of the universe ; namely, 
that there are such things as parallel cases, that 
what happens once will happen again, and not 
only again but always." — Yol. i, p. 370. 

It is evident that Mr. Mill has thoroughly 
elaborated the opinion, for he has profoundly 
criticised the statement of it as made by Eeid 
and Stewart, namely, that it is an intuitive con- 
viction that the future will be as the present. 
He remarks : " Time, in its modification of past, 
present, or future, has nothing to do either with 
the belief itself or the grounds of it. We be- 
lieve that fire will burn to-morrow, because it 
burned to-day and yesterday; but we believe 
on precisely the same grounds, that it burned 
before we were born, and that it burns at this 
very day in Cochin China. It is not from the 
past to the future, as past and future, that we 
infer, but from the known to the unknown, from 
facts observed to facts unobserved, from what 
we have perceived or have been directly con- 
scious of, to what has not come within our ex- 
perience. In this last predicament is the whole 
region of the future, but also the vastly greater 
portion of the present and the past." 



THE PHILOSOPHY OF INDUCTION. 131 



THE ERROR OF MILL. 

Thus far Lis criticism is just ; but in wLat 
follows Le denies that this principle is intuitive, 
and Lerein lies the whole error of his system. 
His empiricism forbids him to acknowledge that 
any universal principles, even the first principles 
of mathematics, are intuitive. He says : " What- 
ever be the most proper mode of expressing it, 
the proposition that the course of nature is uni- 
form, is the fundamental principle or general 
axiom of induction. It would yet be a great 
error to consider this large generalization as any 
explanation of the inductive process. On the 
contrary, I hold it to be an instance of induc- 
tion, and induction by no means of the most 
obvious kind. Far from being the first induc- 
tion we make, it is one of the last, or, at all 
events, one of those which are latest in attain- 
ing strict philosophical accuracy. As a general 
maxim, indeed, it has scarcely entered the 
minds of any but philosophers, nor even by 
them, as we shall have many opportunities of 
remarking, have its extent and limits been al- 
ways justly conceived. It is this principle, 
though so far from being our earliest induction, 



132 ELEMENTS OF LOGIC. 

which must be considered as our warrant for all 
others in this sense, that unless it were true, all 
other inductions would be fallacious." 

Thus this ingenious reasoner disclaims what 
he at first seemed to affirm. He disclaims 
making this principle any explanation of the 
process of induction as being founded upon it, 
or proceeding through it ; but he now regards 
it as only the sine qua non of correct induction, 
so that no induction could be valid were its 
truth not admitted! And why? Because he 
thinks this principle is itself an induction, and 
that not the earliest in science. But if so, how 
could the earliest inductions have been made if 
their truth depends wholly upon this as their 
" fundamental principle ?" And if itself be an 
induction how could it be made at all '? It then 
must have been founded upon itself, or else 
here is one induction, and that the greatest of 
all, which is not formed on this principle. Good 
reason in these paralogisms to modify his state- 
ment! But take his qualified statement, that 
this late induction is the warrant of all other 
inductions, then it follows that all scientific in- 
ductions up to the time when this was formed, 
were without any warrant ; and that warrant 



THE PHILOSOPHY OF INDUCTION. 133 

itself is without any warrant, except it be war- 
ranted by itself; and if this be impossible, then 
itself and all other inductions warranted by it 
are without authority! 

But if we read on we shall find that what he 
calls "warrant in a certain sense" is what all 
who believe in deductive reasoning will call 
proof: "Archbishop Whately has well remarked 
that every induction is a syllogism, with the 
major premise suppressed ; or, as I prefer- to 
express it, that every induction may be thrown 
into the form of a syllogism by supplying a 
major premise. If this be actually done, the 
principle which we are now considering, that 
of the uniformity of the course of nature, will 
appear as the ultimate major premise of all in- 
ductions, and will, therefore, stand to all in- 
ductions in the relation in which, as has been 
shown at so much length, the major premise 
always stands to the conclusion, not contribut- 
ing at all to prove it, but being a necessary con- 
dition of its being proved, since no conclusion 
is proved in which there cannot be found a true 
major premise." 

But why will not Mr. Mill allow that a true 
major premise of a true syllogism proves its con- 



134 ELEMENTS OF LOGIC. 

elusion ? Because the major premise contains the 
conclusion, and itself was formed by the addition 
of particulars, or induction from particulars of 
which that very conclusion was one. Passing 
this for the present, it is enough for our purpose 
that he admits that the principle of the uniform 
course of nature is the foundation of every in- 
duction in the very sense in which the major 
premise of a valid argument is the proof of its 
conclusion. 

INDUCTION FOUNDED ON INTUITION. 

The question now is, Where did we get that 
fundamental principle? It is absurd to con- 
sider it an induction, as we have seen, on Mr. 
Mill's own principles ; it must then be a deduc- 
tion or an intuition. It cannot be a deduction, 
for, as Mr. Mill has clearly seen, that would 
suppose a principle beyond it more general 
from which it was derived. It is an intuition, 
and is given by the reason in its primitive un- 
foldings, and on the very first occasion of the 
recurrence of any cause whose effect we have 
experienced, or of any cause similar to that 
primary cause. We see its manifestations in 
the very first rational actions of the child. Let 



THE PHILOSOPHY OF INDUCTION. 135 

the child put his finger upon a coal of fire, and 
he learns by experience that it causes pain. 
Can you get him voluntarily to touch it a second 
time? He sees another similar coal beside it; 
can you get him to touch that? He will no 
sooner touch the second than the first. Why 
not, seeing that he has no experience but that 
the first coal was once the cause of pain ? He 
knows by experience nothing about its power 
to burn a second time, and nothing at all about 
the power of the second coal to burn. The 
only explanation is, that his reason obliges him 
to conclude as he does ; and this law of the 
reason, this principle of mental order, when 
rendered into language, is the belief that like 
causes produce like effects. It is the province 
of the philosopher to look at this necessary 
movement of the reason and to abstract from 
it the axiom involved in it, and to lay it as the 
basis of all formal disquisitions upon the laws 
of nature. But the child is guided, nay, he is 
governed by it in all his future inductions. It 
transpires in the reason immediately after that 
great first principle of causality, that every 
event has a cause, which is as early as our first 
consciousness of sensation, and which is the oc» 



136 ELEMENTS OF LOGIC. 

casion of our primitive ideas of the external 
world, and of God, the cause of causes, and lays 
the foundation of all science. 

'Nov is the principle of uniform causation in 
the human reason alone ; it belongs as much to 
the instinct of animals of every grade — the fish, 
the bird, the insect, seems infallibly guided by 
it. It pervades the whole animated world, which 
without it, would rush on instant destruction. 
Indeed, the instinct of animals goes beyond this, 
and reveals the causative character of many 
objects before any experience can take place of 
their power to bless or to harm. It is not so 
with man ; he must test everything himself, or 
be taught by those who have tested. A babe 
will as soon put his hand into a flame as snatch 
at a bouquet of flowers; he will chew the 
deadly herb as fearlessly as the lamb would 
pluck the tender grass. 

HUME'S OPINION. 

This fact has been noticed by Mr. Hume with 
an eagerness which characterizes his devotion 
to empiricism. He then takes occasion to 
wonder, with an air of delighted skepticism, 
how it is, after learning thus the particular 



THE PHILOSOPHY OF INDUCTION. 137 

character of causes, we can infer they will con- 
tinue to produce the same effects. 

"All our reasoning on matters of fact seems 
to be founded on cause and effect. By means of 
this relation alone we can go beyond the evi- 
dence of our memory and senses. If you were 
to ask a man why he believes any matter of 
fact which is absent ; for instance, that his 
friend is in the country or in France, he would 
give you a reason, and this reason would be 
some other fact, as a letter received from him, 
or a knowledge of his former resolution. A 
man finding a watch, or any other machine, 
on a desert island, would conclude that there 
had once been men in that island. All our 
reasonings concerning facts are of the same 
nature. ... If we would satisfy ourselves, 
therefore, concerning the nature of that evi- 
dence which assures of matters of fact, we must 
inquire how we came at the knowledge of cause 
and effect. I shall venture to affirm, as a gen- 
eral proposition, which admits of no exception, 
that the knowledge of this is not in any instance 
attained oy reasonings a priori, but arises en- 
tirely from experience, when we find any par- 
ticular objects are conjoined with each other. 



138 ELEMENTS OF LOGIC. 

Let any object be presented to a man of ever 
so strong natural reason and abilities, if that 
object be entirely new to him, he will not be 
able by the most accurate examination of its 
sensible qualities to discover any of its causes 
or effects. Adam, though his rational faculties 
be supposed at the very first entirely perfect, 
could not have inferred from the fluidity and 
transparency of water that it would suffocate 
him, or from the light and warmth of fire that 
it would consume him." 

All this we see no reason to dispute; but 
when he advances to the conclusion that it is 
by repeated or customary experiences that we 
discover the uniformity of causation, we find 
him as blind to the real working of the human 
reason as he would be blind to the operation of 
animal instincts if he should affirm that all 
animals, like man, discover all noxious food and 
other hurtful causes by experience. But let 
Mr. Hume speak for himself upon this point : 
" As to past experience, it can be allowed to give 
direct and certain information of those precise 
objects only and that precise period of time 
which fell under its experience; but why this 
experience should extend to future times and to 



THE PHILOSOPHY OF INDUCTION. 139 

other objects, which, for aught we know, may 
be only in appearance similar; this is the main 
question on which I insist. The bread which I 
formerly ate nourished me ; that is, a body of 
such sensible qualities has induced secret 
powers. But does it follow that other bread 
must also nourish me at another time, and that 
like sensible qualities must always be attended 
with like secret powers? The consequence 
seems to be no wise necessary. At least it 
must be acknowledged that there is here a con- 
sequence drawn by the mind, that there is a 
certain step taken, a process of thought, or in- 
ference, which wants to be explained. These 
two propositions are far from being the same. 
I have found that such an object has always 
been attended with such an effect, and I foresee 
that other objects, which are in appearance 
similar, will be attended with similar effects. I 
shall allow, if you please, that one proposition 
may justly be inferred from the other. I know, 
in fact, that it always is inferred. But if you 
insist that the inference is made by a chain 
of reasoning, I desire you to produce that 
reasoning." 

Eureka ! good Mr. Hume, we have found out 



140 ELEMENTS OF LOGIC. 

that reasoning, that connecting principle which 
you despaired of finding. It lay just before 
your eyes when you penned the observation 
that one proposition is always inferred from the 
other. Do you not see that you here struck 
upon a law of the reason by which it is neces- 
sitated to operate thus, and that this law ex- 
pressed in language is the axiom, Like causes 
produce like effects? or, as it is generally stated, 
The course of nature is uniform. "What men 
always think and must think is a primary and 
essential truth, an ultimate principle of reason. 
But Mr. Hume has objected to this origin of 
the principle. "Were it the offspring of the 
reason, an intuition, it would be as perfect at 
first and from one instance, as after ever so long 
a course of experience. But the case is far 
otherwise. Nothing is so like as eggs ; yet no 
one, on account of this apparent similarity, ex- 
pects the same taste and relish in all of them. 
It is only after a long course of experiments in 
any kind that we attain a firm reliance and 
security with regard to a particular event. 
JSTow, where is that process of reasoning which 
from one instance draws a conclusion so differ- 
ent from that which it infers from a hundred 



THE PHILOSOPHY OF INDUCTION. 141 

instances, that are nowise different from that 
single one? This question I propose as much 
for the sake of instruction as with an intention 
of raising difficulties. I cannot find, I cannot 
imagine any such reasoning." 

It would be easy to turn off this question 
with a joke, especially as the example of the 
eggs is so egregiously puerile ; but it is due to 
the candor of Mr. Hume to treat it seriously, 
nay, to admit that the question is one of great 
importance, and leads to the true science of in- 
duction. It is not true that bodies having the 
same or similar qualities produce different ef- 
fects ; the eggs that have a different taste are 
different in some particulars, and this is usually 
sufficiently manifest in eggs ; and if your eyes 
fail to see it, a microscope will abundantly re- 
veal it. Just here opens to our view the ap- 
propriate sphere of induction, as far as it may 
be properly distinguished from deduction ; its 
office is to analyze phenomena, to mark the 
different qualities of objects, and to ascertain 
their precise effects; but when you have cer- 
tainly determined what qualities in any case 
produce what effects, one single instance of 
causation is sufficient for the widest generali- 



142 ELEMENTS OF LOGIC. 

zation. Show me the property of the magnet 
which attracts iron, and I hesitate not to pre- 
dict that whenever and wherever that quality 
appears, in like circumstances, it will be followed 
by the same effect. But if I have not been 
careful in my observations and mistaken some 
other property for the real one, then most cer- 
tainly I shall make a false prediction, and the 
event will expose the error. It is not in the 
reason, which assures me intuitively that like 
causes produce like effects, but in my observa- 
tion. 

MERIT OF MILL. 

Science is under no greater obligation to any 
writer of the present age than to Mr. John 
Stuart Mill, for the profound and elaborate ex- 
position of the grounds and process of induction 
which he has given to the world. " There is no 
event," he remarks, " happening in the uni- 
verse, which is not connected by an invariable 
sequence with some one or more of the phenom- 
ena which preceded it." " If we knew all the 
agents which exist at the present moment, their 
collocation in space,. and their properties, or in 
other words, the laws or modes of their agency, 



THE PHILOSOPHY OF INDUCTION. 143 

we could predict the whole subsequent history 
of the universe ; at least, unless some new vo- 
lition of a power capable of controlling the 
universe should supervene. And if any par- 
ticular state of the universe should ever recur a 
second time, (which, however, all experience 
combines to assure us will never happen,) all 
subsequent states would return too, and history 
would, like a circulating decimal of many 
figures, periodically repeat itself. 

"Jam redit et virgo, redeunt Saturnia regna, 
Alter erit turn Tiphys, et altera quse vehat Argo 
Delectos heroas : erunt quoque altera bella, 
Atque itcrum ad Troiam niagnus mittetur Achilles." 

Such undoubtedly is the order of the universe, 
with the single exception of the free-will of 
moral agents. But Mr. Mill makes no such 
exception, for he holds that human volitions are 
so far controlled by motives that a man's actions 
as inevitably result from his character as any 
effect follows a cause ; and if we thoroughly 
knew his character we could certainly predict 
how he would act in any supposable case. But 
this we repudiate, for this reason, among many 
which cannot now be mentioned, that the same 



144 ELEMENTS OF LOGIC. 

view must apply to the divine mind ; and then 
it would follow that the universe, like a circu- 
lating decimal, actually has been, and will be 
produced and destroyed, again and again, for- 
ever. For God is the same in character ; and 
if, when nothing was but he, his power pro- 
duced the present universe, it was but the type 
of a past and a coming eternity. Plato's rem- 
iniscences are resurrections ; and not only the 
ideas that now are have been before, but we 
ourselves, the world's millions, and all their 
various histories, have been before as now, and 
will be as they now are, again and again, for- 
evermore. But, aside from free agents, the 
idea of Mr. Mill is as true as it is sublime ; and 
it illuminates and explains the problem of in- 
duction. The law of causation binds together 
the universe, and the only difficulty is to dis- 
cover that chain amid the shifting, and veering, 
and multitudinous phenomena that move about 
it and upon it ; but if you can strike that chain 
at one point it will vibrate throughout its whole 
direction. " The order of nature, as perceived 
at first glance, presents at every instant a 
chaos, followed by another chaos. We must 
decompose each chaos into single facts. "We 



THE PHILOSOPHY OF INDUCTION. 145 

must learn to see in the chaotic antecedent a 
multitude of distinct antecedents, and in the 
chaotic consequent a multitude of distinct con- 
sequents." What then ? We have to determine 
which particular antecedent is followed by 
which consequent, and which consequent is 
produced by which antecedent; then, by the 
simplest ratiocination, whose major premise is 
the principle of causality, furnished by the 
reason, we generalize the fact, or, in other 
words, infer a law of nature. To make the 
requisite analysis we need to observe and ex- 
periment ; and we require no aid but the simple 
rules of arithmetic, except in those cases where 
the effects of various causes are mixed together, 
as the curvilinear motion of the rocket, which 
is the result of various causes. Here we re- 
quire the aid of the higher mathematics to de- 
termine the proportion in which the causes 
mingle in producing the effect. But all mathe- 
matics is deductive. Hence, nowhere in induc- 
tion, throughout its whole circuit, can jou find 
any new principle of inference. Inference, 
therefore, is always one and the same ; it is a 
passage of the thought from the more general 

to the less general, or to the particular ; and 
10 



146 ELEMENTS OF LOGIC. 

never vice versa, from the particular or from 
particulars, however numerous, to the general. 
I repeat, you may sum them up, and call them 
by a general name ; but that is no inference, 
no induction, nothing but generalization. 

CONCLUSION OF THE ARGUMENT. 

Thus, it is demonstrated that the process by 
which we discover the laws of nature is funda- 
mentally a deductive process ; and that we are 
as much indebted to the reason for the major 
premise as we are indebted to experience for 
the minor premise. 

ARISTOTLE VINDICATED. 

It is owing to a misapprehension of the in- 
tuitive developments of the reason that some 
modern philosophers have rejected the syllo- 
gism as a type of ratiocination. They suppose 
its major premise is a general truth obtained by 
a summation of particulars ; and, consequently, 
to deduce one of these particulars from the 
general is to reason in a circle. But, great as 
the mystery of the reason may appear, we hold 
it to be the source of general principles, and it 
gives them to us as by revelation. So struck 



THE PHILOSOPHY OF INDUCTION". 147 

was Cousin with this function of reason that he 
seemed well-nigh beside himself, and almost 
ready to bow down and worship it as a portion 
of divinity ; and Plato, at the dawn of philoso- 
phy, declared, "It is the gift of the gods to 
man, which, as I conceive, they sent down by 
some Prometheus in a blaze of light." But it 
is no enthusiasm to say that the reason is the 
brightest aspect of the image of God in man. 
Were the human mind destitute of this power 
of intuition it would be impossible to vindicate 
the logic of Aristotle. This he clearly saw and 
stated in his exposition of the process of deduc- 
tion. Indemonstrable truths, he affirms, make 
the basis of all reasoning ; for if your premises 
be demonstrated, then they must have been de- 
monstrated by something beyond them, and if 
they were demonstrable though not demon- 
strated, it only extends the chain indefinitely 
back. Hence there must be indemonstrable 
truths at the foundation of every reasoning pro- 
cess, or it is without foundation. And these 
indemonstrable truths are particular intuitions 
of sense, of consciousness, and of the reason, and 
also the general intuitions or principles of the 
reason. Thus sense gives us direct knowledge 



148 ELEMENTS OF LOGIC. 

of the qualities of bodies ; consciousness, of the 
phenomena of mind ; and reason, ideas of sub- 
stance, space, time, cause, right and wrong, and 
the principles of causality, mathematical prin- 
ciples, etc. The principle of contradiction, 
namely, a thing cannot be and not be at the 
same time, Aristotle considered the first of these 
indemonstrable principles, which lay at the 
foundation of demonstration. 

ERROR OF THE SCHOOLMEN. 

The error of the schoolmen, which plunged 
them into the vortex of abstract speculation, 
and for which Plato is to be blamed rather than 
Aristotle, was in the supposition that all truth 
lay wrapped up in a priori principles, and 
could be educed by ratiocination : they failed 
to perceive that they yielded no consequences 
of scientific value, but as they were attached to 
facts. Bacon reclaimed science from folly by 
turning her eye upon the actual phenomena of 
nature. But it is an illusion as great as that of 
the scholastics, to suppose that facts can of 
themselves give science ; for they are as incon- 
sequential without the principles of intuition as 
these are barren without them; they lie scat- 



THE PHILOSOPHY OF INDUCTION. 149 

tered about like pobbles on the shore, until they 
are bound together by some a priori principle 
or general truth ; then we see in them the path 
of the mighty laws that clasp and encircle the 
universe. A falling apple sheds a ray of light 
through immensity, and a drop of rain marking 
the clay pours its illuminations down the chasms 
of a past eternity. 

And is not here the answer to Mr. Mill's earn- 
est inquiry: " Why is a single instance in some 
cases sufficient for a complete induction ; while in 
others, myriads of concurring instances, without 
a single exception, known or presumed, go so 
little way toward establishing a universal prop- 
osition?" The difference in the cases is that 
the former stands in the relation of cause and 
effect, and the latter does not. " Whoever," he 
adds, "can answer this question knows more 
than the wisest of the ancients, and has solved 
the problem of induction." Let him add the 
true theory of the origin of primary axioms to 
his own incomparable analysis of induction, 
and he may demand the palm. Take away the 
a priori principles from induction, and you 
cover with clouds the whole process, and the 
long array of the sciences dependent upon it ; 



150 ELEMENTS OF LOGIC. 

restore these ideas and the movement is attended 
with certainty, as far as certainty can belong to 
human knowledge. 

I say as far as certainty belongs to human 
knowledge, because, after all, it must be con- 
fessed that absolute knowledge is not for man. 
In its very depths what is our knowledge but 
faith % When we talk of certainty what do we 
mean ? Certainty for an individual is but his 
necessary belief; human certainty is the neces- 
sary and universal belief of the race. In 
heaven itself certainty is absolute only in the 
Throne of Light ; the knowledge of the loftiest 
archangel nearest that Throne is but a cloudless 
belief, forced upon his understanding by its own 
subjective laws. God only knows, and knows 
he knows ; God only is light. 

SECOND CAUSES. 

This leads us to remark, that the problem of 
induction being only a question of causation, it 
matters not what theory any one adopts in re- 
spect to second causes, if he admits that no 
event is without a cause, and like causes pro- 
duce like effects, that is, what seems to us to be 
causes. To me, however, there is no more diffi- 



THE PHILOSOPHY OF INDUCTION. 151 

culty in supposing that God has put a causative 
power in nature distinct from his own, than 
that he has constituted nature, both matter and 
mind, distinct from his own essence. If matter 
exists with its various elements distinct from 
the divine nature, though not independent of 
it, why may we not suppose that God has en- 
dued it with a motive property as well as other 
properties? Secondary causes are the general 
belief of mankind as well as secondary natures. 
Still, you may take either hypothesis ; you may 
think it was the electric fluid which struck the 
oak when it fell, blasted and blazing with light- 
ning, or you may regard it as the stroke of the 
divine thought or volition, and think that all 
other events are, in like manner, the extempo- 
raneous movements of the all-pervading mind 
of Deity. Yet if your reason obliges you to 
believe that they proceed upon the principles 
of causality, then induction is the same, and the 
certainty of its results is the same. Proceeding 
upon a priori and empirical data conjointly, 
the process is not to be doubted until the facul- 
ties of observation and reason are doubted ; and 
when they are doubted the mind is ruined, and 
the light of knowledge is set forever. 



II. 

MISCELLANEOUS EXAMPLES EOR 
PRACTICE. 

LESSON I. 

1. That which is followed by repentance is 

not to be desired ; 
Some pleasures are followed by repentance ; 
Therefore, some pleasures are not to be 

desired. 

2. If the world existed from eternity there 

would be records prior to the Mosaic; 

and if it were produced by chance it 

would not bear marks of design ; 
But there are no records prior to the 

Mosaic, and the world does not bear 

marks of design ; therefore, 
The world neither existed from eternity, nor 

is it the work of chance. 

3. Every dispensation of Providence is bene- 

ficial ; 
Afflictions are dispensations of Providence ; 
Therefore, they are beneficial. 



EXAMPLES FOR PRACTICE. 153 

4. If there is a God he ought to be wor- 

shiped ; 
But there is a God ; 
Therefore, he ought to be worshiped. 

5. If God is infinitely wise, and acts with per- 

fect freedom, he does nothing but what is 

best; 
But God is infinitely wise, and acts with 

perfect freedom ; 
Therefore, he does nothing but what is best. 

6. If God were not a Being of infinite good- 

ness, neither would he consult the happi- 
ness of his creatures ; 

But God does consult the happiness of his 
creatures ; 

Therefore, he is a Being of infinite good- 
ness. 

7. The world is either self-existent, or the work 

of some finite, or of some infinite being ; 
But it is not self- existent, nor the work of a 

finite being ; 
Therefore, it is the work of an infinite 
Being. 

8. No deceitful man merits confidence ; 
All honest men merit confidence ; 
Therefore, no honest man is deceitful. 



154 ELEMENTS OF LOGIC. 

9. Every human virtue is to be sought with 
diligence ; 
Prudence is a human virtue " f 
Therefore, prudence is to be sought dili- 
gently. 
10. Everything base should be avoided ; 
Some pleasures are base ; 
Therefore, some pleasures should be avoided. 

lesson n. 

1. He who follows evil counsel will meet with 

trouble ; 
Rehoboam followed evil counsel ; 
Therefore, Rehoboam met with trouble. 

2. No good citizen will violate the laws of God 

and man ; 
Duelists do that which violates the laws 

of both God and man ; 
Therefore, duelists are not good citizens. 

3. Things offensive to delicacy should not be 

used; 
Therefore, some words should not be used. 

4. That which is prudent is commendable ; 
Moderation is prudent ; 

Therefore, moderation is commendable. 



EXAMPLES FOR PRACTICE. 155 

5. We are bound to set apart one day in 

seven for religions duties, if the fourth 
commandment is obligatory on us; but 
we are bound to set apart one day in 
seven for religious duties ; and hence it 
appears that the fourth commandment is 
obligatory on us. 

6. A desire to gain by another's loss is a viola- 

tion of the tenth commandment ; all 
gaming, therefore, since it implies a de- 
sire to profit at the expense of another, 
involves a breach of the tenth command- 
ment. 

7. All the fish that the net inclosed were an 

indiscriminate mixture of various kinds ; 
those that were set aside and saved as 
valuable, were fish that the net inclosed ; 
therefore, those that were set aside and 
saved as valuable were an indiscriminate 
mixture of various kinds. 

8. No one who lives with another on terms of 

confidence is justified on any pretense in 
killing him; Brutus lived on terms of 
confidence with Cesar ; therefore, he was 
not justified, on the pretense he pleaded, 
in killing him. 



156 ELEMENTS OF LOGIC. 

9. Seeing that I have experienced calamity in 
the snares of pleasure, I should abandon 
its pursuit. 
10. The principles of justice are variable ; the 
appointments of nature are invariable ; 
therefore, the principles of justice are no 
appointment of nature. 

LESSON III. 

1. All good Christians are saved ; 
All good Christians have sinned ; 
Therefore, some who have sinned will be 

saved. 

2. Knowledge is better than riches ; 
Virtue is better than knowledge ; 
Therefore, virtue is better than riches. 

3. Christianity requires us to believe what the 

apostles wrote ; 
St. Paul is an apostle ; 
Therefore, Christianity requires us to believe 

what St. Paul wrote. 

4. It is necessary that a general should under- 

stand the art of war ; 
But Caius did not understand the art of war ; 
Therefore, it is necessary that Caius should 

not be a general. 



EXAMPLES FOR PRACTICE. 157 

5. A total eclipse of the sun would cause dark- 

ness at noon ; 
It is possible that the moon at that time may 

totally eclipse the sun ; 
Therefore, it is possible that the moon' may 

cause darkness at noon. 

6. The fogs vanish as the sun rises ; 

But the fogs have not yet begun to vanish ; 
Therefore, the sun is not yet risen. 

7. The sun is a senseless being ; 

What the Persians worshiped is the sun ; 
Therefore, what the Persians worshiped is a 
senseless being. 

8. If every creature be reasonable every brute 

is reasonable ; 
Bnt no brute is reasonable ; 
Therefore, no creature is reasonable. 

LESSON IV. 

1. God is omnipotent ; 

An omnipotent being can do everything 

possible ; 
He that can do everything possible can do 

whatever involves not a contradiction ; 
Therefore, God can do whatever involves 

not a contradiction. 



158 ELEMENTS OF LOGIC. 

2. If we love any person, all emotions of hatred 

toward him cease ; 

If all emotions of hatred toward a person 
cease, we cannot rejoice in his mis- 
fortunes ; 

If we rejoice not in his misfortunes, we cer- 
tainly wish him no injury ; 

Therefore, if we love a person we wish him 
no injury. 

3. A thinking substance is a spirit; 
A spirit has no extension ; 

What has no extension has no parts ; 
What has no parts is indissoluble ; 
Therefore, the mind is immortal. 

4. If God did not create the world perfect in 

its kind, it must either proceed from want 
of inclination or from want of power ; 

But it could not proceed from want of in- 
clination or from want of power ; 

Therefore, God created the world perfect in 
its kind, or, which is the same thing, it is 
absurd to say that he did not create the 
world perfect in its kind. 

5. Whatever is immaterial is indissoluble ; 
The mind of man is immaterial ; 
Therefore, the mind of man is indissoluble. 



EXAMPLES FOE PRACTICE. 159 

6. Whatever perceives, judges, and reasons, is 

a thinking substance; 
The human mind perceives, judges, and 

reasons ; 
Therefore, the human mind is a thinking 

substance. 

7. Things equal to the same thing are equal to 

one another; 
Therefore, these two triangles, each equal 
to the square of a line of three inches, 
are equal between themselves. 

8. What is not a being, since it can have no 

attributes, can be no agent nor act, cannot 
produce anything ; 
What is called nothing is not a being, has 
no attribute, is not an agent, nor can it 
act; therefore, what is called nothing 
cannot act or produce anything. 

9. The order and constitution of things estab- 

lished and maintained in the universe, is 

the law of Supreme intelligence ; 
Nature is the order and constitution of 

things established and maintained in the 

universe ; therefore, 
Nature is the law of Supreme intelligence. 



160 ELEMENTS OF LOGIC. 

LESSON V. 

1. No man can possess power to perform im- 

possibilities ; 

A miracle is an impossibility ; 

Therefore, no man can possess power to per- 
form a miracle. 

2. "War is the source of numerous evils ; 
Some wars are just ; therefore, 

Some just actions are the source of numer- 
ous evils. 

3. Protection from punishment is plainly due 

to the innocent ; therefore, as you main- 
tain that this person ought not to be 
punished, it appears that you are con- 
vinced of his innocence. 

4. All the most bitter persecutions have been 

religious persecutions ; among the most 
bitter persecutions were those which oc- 
curred in France during the Revolution ; 
therefore, they must have been religious 
persecutions. 

5. Of two evils the less is to be preferred ; oc- 

casional turbulence, therefore, being a 
less evil than rigid despotism, is to be 
preferred to it. 



EXAMPLES FOR PRACTICE. 161 

6. The early and general assignment of the 

Epistle to the Hebrews to St. Paul as its 
author, must have been either from its 
professing to be his, and containing his 
name, or from its really being his ; since, 
therefore, the former of these is not the 
fact, the epistle must be Paul's. 

7. All the miracles of Jesus would fill more books 

than the world could contain ; the things 
related by the evangelists are the miracles 
of Jesus ; therefore, the things related by 
the evangelists would fill more books 
than the world could contain. 

8. According to theologians, a man must 

possess faith in order to be acceptable to 
the Deity ; now he who believes all the 
fables of the Hindoo mythology must 
possess faith ; therefore, such a one 
must, according to theologians, be ac- 
ceptable to the Deity. 
.9. If Abraham were justified, it must have 
been either by faith or by works ; now, 
he was not justified by faith, (according 
to St. James,) nor by works, (according 
to St. Paul ;) therefore, Abraham was not 

justified. 

11 



162 ELEMENTS OF LOGIC. 

10. He who cannot possibly act otherwise than 
he does has neither merit nor demerit in 
his action ; a liberal and benevolent man 
cannot possibly act otherwise than he 
does in relieving the poor ; therefore, 
such a man has neither merit nor demerit 
in his action. 



LESSON VI. 

1. Smollet, in a town in France, having met at 
an inn with a scolding chambermaid and an 
awkward red-haired hostler, who had engrossed 
his whole attention, immediately wrote in his 
journal: "The men in this town are all red- 
haired, and the women are all scolds." 

2. The Stoics proved that the world was a great 
animal, thus : That which has the use of reason 
is better than that which has not. Now, there 
is nothing better than the world ; therefore, the 
world has reason and is a great animal. 

3. The Sophists used the following argument 
against marriage : If a woman that marries be 
lovely she will create jealousies ; if she be ugly 
she will not delight ; therefore, it is not good to 
marry. 



EXAMPLES FOR PRACTICE. 163 

4. An Irishman, hearing much of the charms of 
a feather bed, took a feather and laid it on a 
rock for a pillow. He awoke with a headache. 
" Arrah," said he, "if these be your feathers give 
me my straw." 

5. "Warm countries alone produce the Banian- 
tree. Spain is a warm country ; therefore, 
Spain produces the Banian-tree. 

6. A canal boat was passing under a bridge, 
and some one on deck cried out, "Look out!" 
A Dutchman lying in his berth heard the cry, 
and stuck his head out of the window, and re- 
ceived a severe blow on his forehead. "Vat 
for," cried he, in a passion, " did you tell me to 
'look out?' vy did you not tell me to 'look 
in V " 

7. As I would not trifle with the prejudices of 
the poor, because it is illiberal, so I would not 
always yield to them, because it is unwise. 

8. Books are seldom correct, because human 
nature is fallible. 

9. Fugitive cant, which is always in a state of 
increase or decay, cannot be regarded as any 
part of the durable materials of a language, and 
therefore must be suffered to perish with other 
things unworthy of preservation. 



164 ELEMENTS OF LOGIC. 

10. Pleasures are deceitful; therefore, young 
men should curb their inclinations. 



LESSON VII. 

Let the learner analyze the following, giving, 
1st, the terms; 2d, the propositions; 3d, the 
syllogisms. 

Ye men of Athens, I perceive that in all 
things ye are too superstitious. For as I passed 
by and beheld your devotions I found an altar 
with this inscription : " To the Unknown God." 
"Whom, therefore, ye ignorantly worship him de- 
clare I unto you. God that made the world and 
all things therein, seeing that he is Lord of 
heaven and earth, dwelleth not in temples made 
with hands; neither is worshiped with men's 
hands, as though he needed anything, seeing 
he giveth to all life, and breath, and all things ; 
and hath made of one blood all nations of men 
for to dwell on all the face of the earth, and 
hath determined the times before appointed, 
and the bounds of their habitation ; that they 
should seek the Lord, if haply they might feel 
after him and find him, though he be not far 
from every one of us : 



EXAMPLES FOR PRACTICE. 165 

For in him we live, and move, and have our 
being ; as certain, also, of your own poets have 
said, for we are also his offspring. 

Forasmuch, then, as we are the offspring of 
God, we ought not to think that the Godhead is 
like unto gold, or silver, or stone, graven by art 
and man's device. 

And the times of this ignorance God winked 
at, but now commandeth all men everywhere to 
repent ; 

Because he hath appointed a day in the 
which he will judge the world in righteousness 
by that man whom he hath ordained ; whereof 
lie hath given assurance unto all men in that he 
hath raised him from the dead. 

LESSON VIII. 

Arguments from unpublished documents. 

1. If the Mosaic doctrine of the absolute crea- 

tion of the world out of nothing, by the 
divine decree, were unreasonable, it 
would have shocked the common mind. 

2. If Pantheism be true, and all things are but a 

development of the Deity, then the idea 
of cause in the human mind is an il- 



166 ELEMENTS OF LOGIC. 

lusion, for in that case it is nowhere fully 
realized, as modifications are not abso- 
lute causations. 

3. Though we cannot, with Plato and Cousin, 

regard the reason in man as itself divine, 
it is certainly perfect ; and is, therefore, 
as a perfect creation, evidence of a per- 
fect Creator. 

4. No interpretation of the Bible is to be con- 

sidered correct which is directly opposed 
to the absolute principles of reason, for 
this would be suicidal, inasmuch as every 
argument for the divine inspiration of the 
Bible is based upon those very prin- 
ciples. 

5. If the New Testament be not a true history 

of Christ, it is the greatest romance in all 
literature ; and if it be the greatest ro- 
mance ever written, its author could not 
have been unknown to his cotempo- 
raries. 

6. If the story of the resurrection be true, the 

Christian religion is proved to be of di- 
vine origin ; if it be false, no explanation 
can be given of the sudden and extensive 
spread of the Christian faith. 



EXAMPLES FOR PRACTICE. 167 

7. The Bible must be of divine origin, for its 
production isbeyond all example of human 



The remainder are from notes of Dr. Whedon. 

8. Every necessary, universal, and perpetual 

idea is a truth ; 
Immortality is such an idea ; 
Therefore, immortality is a truth. 

9. Nothing is to be held eternal which we can 

rationally conceive once to have not ex- 
isted, and the infinite space to be vacant 
of it. 

10. Nothing is by the laws of the mind to be 
held as having no beginning, which we 
can rationally conceive to have once non- 
existed and then begun. Now of the 
visible material world we can conceive 
space to have been empty, we can con- 
ceive that it once nonexisted and then 
began. Not so of space or of creative 
mind. In order to the world's beginning, 
these must have preceded and never 
have had a beginning. 



168 ELEMENTS OF LOGIC. 

11. The regular organization of the world must 

either be eternal, or formed without de- 
sign, or formed by design ; 

The regular organization of the world can- 
not be eternal ; for geology shows it to be 
composed of elements once inorganic. 

The regular organism of the world cannot 
be without design, for no complex adjust- 
ment of parts to accomplish an end can 
exist without design. 

12. The regular organization of the world is by 

design, for it accords with all the laws of 
design, and with nothing else that we 
know. 

LESSON IX. 

Supposed Exceptions to Rules. 
Hamilton, Thompson, and our own country- 
man, Mahan, and others, have suggested several 
alterations in the forms of Logic, as left by 
Aristotle ; but ^vith deference to these original 
thinkers, I consider them unnecessary and in- 
expedient. To try the skill of the advanced 
student, and to make this book as complete 
as may be, without an adequate discussion 
of these topics, the present lesson will contain 



EXAMPLES FOR PRACTICE. 169 

specimens of those propositions and arguments 
which have been supposed to be exceptions to 
the rules and to require a re-formation of the 
science. 

Eight Classes of Propositions •, instead of the 
four, A, E, 7", 0, of Aristotle. 

1. Toto-total. All A is all of B. — All men are 

all rational animals. 

2. Toto-partial. All A is some of B. — All men 

are mortal. 

3. Parti-total. Some A is all of B. — Some men 

are all the sailors. 

4. Parti-partial. Some A is some of B. — Some 

men are sailors. 

5. Toto-total. Any A is not any B. — No man is 

a brute. 

6. Toto-partial. Any A is not some B. — No man 

is some brute. 

7. Parti-total. Some A is not any B. — Some 

men are no brutes. 

8. Parti-partial. Some A is not some B. — Some 

men are not some brutes. 
Thompson makes but six. 

A. All plants grow. 

E. ISTo right action is inexpedient. 



170 ELEMENTS OF LOGIC. 

I. Some muscles act without volition. 
O. Some plants do not grow in the tropics. 
U. Common salt is chloride of sodium. 
Y. Some stars are all planets. 

Hamilton and Mahan add : 

o). Some X is not some Y. 
r\. "No X is some Z. 

A is converted into Y. 
E " " E. 

I « " 1. 

O " " 7}. 

U " " IT. 

Y " " A. 

0) " " 6). 

T} " " O. 

If we admit Sir William Hamilton's doctrine 
of the Quantification of the Predicate, namely, 
that if you refer not to the form of expression, 
but to what is meant by it, the predicate has al- 
ways a definite quantity, and the proposition 
way always he converted simply j still this very 
difference between the form of a proposition 
and its meaning, makes it necessary to have 
rules to determine what is the extent of the 



EXAMPLES FOR PEACTICE. 171 

predicate and to govern conversion ; and no 
rules are better than those of Aristotle, if we 
keep in mind the exceptions to the rules I have 
made. (See Section on Distribution.) 

EXAMPLES OF IMMEDIATE INFERENCE. 

These supposed inferences will be found to 
be either the same as the premise in different 
language, or derived from it by means of 
another premise understood, or by conversion. 

IMMEDIATE INFERENCE BY MEANS OF PRIVA- 
TIVE CONCEPTIONS. 

I. The Premise, a Positive Conception. 

A. All the righteous are happy ; 

Therefore, none of the righteous are un- 
happy; 
And, all who are unhappy are unrighteous. 
E. No human virtues are perfect ; 

Therefore, all human virtues are imperfect ; 
And, all perfect virtues are not human. 
I. Some possible cases are probable ; 

Therefore, some possible cases are not im- 
probable ; 
And, some probable cases are not impossible. 



172 ELEMENTS OF LOGIC. 

0. Some possible cases are not probable ; 
Therefore, some possible cases are im- 
probable ; 

And, some improbable cases are not im- 
possible. 
U. The just are [all] the holy ; 

Therefore, all unholy men are unjust ; 
And, no just men are unholy. 
Y. Some happy persons are [all] the righteous ; 
Therefore, all who are unhappy are un- 
righteous ; 
And, no righteous persons are unhappy. 

II The Premise, a Privative* Conception. 
A. All the insincere are dishonest : 

Therefore, no insincere man is honest; 

And, all honest men are sincere. 
E. ~No unjust act is unpunished ; 

Therefore, all unjust acts are punished ; 

And, all acts not punished are just. 

1. Some unfair acts are unknown ; 
Therefore, some unfair acts are not known ; 
And, some unknown acts are not fair. 

O. Some improbable cases are not impossible ; 
Therefore, some improbable cases are pos- 
sible ; 
And, some possible cases are not probable. 



EXAMPLES FOR PRACTICE. 173 

U. The unlawful is the [only] inexpedient ; 

Therefore, the lawful is the expedient ; 

And the lawful is not the inexpedient. 
Y. Some unhappy men are [all] the unright- 
eous; 

Therefore, no happy men are unrighteous ; 

And, some unhappy men are not righteous. 



IMMEDIATE INFERENCE BY ADDED DETERM- 
INANTS. 

A servant is a fellow- creature ; 

Therefore, a servant in suffering is a fellow- 
creature in suffering. 

Yirtue deserves respect, and a servant is a 
fellow-creature ; 

Therefore, a virtuous servant is a fellow- 
creature deserving of respect. 



IMMEDIATE INFERENCE BY COMPLEX CONCEP- 
TION. 

Oxygen is an element, so that the decompo- 
sition of oxygen would be the decomposition of 
an element. 



174 ELEMENTS OF LOGIC. 

IMMEDIATE INFERENCES OF INTERPRETATION. 

All the Gentiles are also called ; that is, all 
other nations, as well as the Jewish, are called. 

Howard exhibited this high philanthropic 
spirit ; 

Therefore, snch philanthropy really exists. 

A is B ; therefore, B exists. 

A is B ; therefore, where A is we find B. 



IMMEDIATE INFERENCE FROM A DISJUNCTIVE 
JUDGMENT. 

All teeth are either incisors, canine, bicuspid, 
or molar ; 

Therefore, the molar teeth are neither incisors, 
canine, nor bicuspid ; 

And, all teeth which are not molar are either 
canine, incisors, or bicuspid. 



IMMEDIATE INFERENCE BY THE SUM OF 
SEVERAL PREDICATES. 

Copper is a metal of a red color and dis- 
agreeable smell and taste, all the properties of 
which are poisonous ; which is highly malleable, 



EXAMPLES FOK PRACTTCE. 175 

ductile, tenacious, with a specific gravity of 
about 8.83; * 

Therefore, a metal of a red color, etc., is 
copper. 



UNFIGURED SYLLOGISM. 

In the unfigured syllogism of Hamilton and 
Mahan the terms compared do not stand to each 
other in the relation of subject and predicate, 
being in the same proposition either both sub- 
jects or both predicates. 

All C and some B are equal ; 

All A and all B are equal ; 

Therefore, all C and some A are equal ; 

Or, C and A are unequal. 

Copperas and sulphate of iron are identical ; 

Sulphate of ii'on and sulphate of copper are 
not identical ; 

Therefore, copperas and sulphate of copper 
ixe not identical. 

All C and all B equal Y ; 

All A and all B do not equal Y ; 

Therefore, C and A are not equal to each 
other. 



176 ELEMENTS OF LOGIC. 

C and B always coexist, or are universally 
compatible ; 

A and B never coexist, or are wholly incom- 
patible ; 

Therefore, C and A never coexist, or are not 
compatible. 

Some of these unfigured syllogisms, upon anal- 
ysis, will be found to contain one or two other 
syllogisms with premises suppressed. In the first 
instance given, "Things equal to the same thing 
are equal to each other" is the implied premise. 

REASONING FROM WHOLES IN COMPREHENSION. 

Sir William Hamilton's discovery is illusory ; 
an individual cannot comprehend a species, nor 
a species a genus. This red rose is both in ex- 
tension and comprehension one. A single rose 
with its own red; it cannot comprehend red 
rose, which is not only this, but that, and all 
other red roses ; and it admits of no inference. 
A thing is itself and not something else how- 
ever like it, much less its class. So triangle 
comprehends not figure, but only the three- 
angled portion. 

THE END. 











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